CONNECT: Ways of writing numbers


 Anthony Lawrence
 2 years ago
 Views:
Transcription
1 CONNECT: Ways of writing numbers SCIENTIFIC NOTATION; SIGNIFICANT FIGURES; DECIMAL PLACES First, a short review of our Decimal (Base 10) System. This system is so efficient that we can use it to write any number we like, no matter how big or how small. But, when numbers get either TOO big or small, then the amount of digits becomes unwieldy. That s where Scientific Notation, Significant Figures and Decimal Places all come in. You probably remember from school that the place value of a number is important because it determines how big the number is. I am sure you also remember the names of all the place values, especially of the whole numbers: millions hundred thousands ten thousands thousands hundreds tens units. Reading from the right (units), each column to the left has been obtained by multiplying by 10 (each column represents a number that is 10 times bigger than the one on its right). For example, 10 is 1 x 10, 100 is 10 x 10, 1000 is 100 x 10 and so on. (Same as 20 is 2 x 10, 350 is 35 x 10.) Going in the other direction, each column to the right has been obtained by dividing the one on its left by 10. The decimal point which goes straight after the units column tells us that we no longer have a whole number, and that the unit has been divided by 10. That s why 0.1 is the same as 1 10, or has been divided by 10 in the same way as = 10, or = 100. The number is moved across a column to make it smaller. So, we get new headings for our place values AFTER (to the right of) the decimal point. 1
2 millions hundred thousands ten thousands thousands hundreds tens units. tenths hundredths thousandths One tenth can be written as or 0.1, a hundredth can be written as or 0.01, and a thousandth can be written as or DECIMAL PLACES Decimal places are the positions of numbers that appear to the right of the decimal point. They can give us a way of stating how accurately we want to measure something. For example, when you fill up the car at the petrol pump, you know that the price of petrol is given to three places of decimals (in cents), yet we round that to 2 places when we pay in fact we even round to the nearest 5 cents. So the calculation that the machine does is accurate right up until the very last step. For example, my car might take 32.4 litres when the price is cents per litre. If we calculate this (and of course you can use your calculator!) we get Thankfully, this is cents, so we need to divide by 100 and get ($) Now, rounding to 2 decimal places (the nearest cent), we look at the 3 rd decimal place that is the 7 and ignore everything that comes after it. If the 3 rd decimal place is 5, 6, 7, 8, or 9, then we round up and we would get $ This is because the 7 is more than halfway up to the next number (this is similar to 327 being closer to 330 than it is to 320). I like to put a little line to the right of the number I m going to round to: Then I look at the next number (7) and work out what to do. Let s say we have an answer to some other calculation and it looks like this: That is too many digits for the answer to make sense in our calculation so let s try to round it to four decimal places. So we look at This time the (Of course, in cash, we would actually pay $45.35.) 2
3 2 to the right of the line tells us to keep the 4 th number just as it is, so we get So our number represents 5 thousand, 8 hundred and ninetyfour point 8 tenths, 7 hundredths, 4 thousandths, 1 ten thousandth. We rounded off the 2 hundred thousandths and 8 millionths! Of course this all depends on how precise we want an answer to be. (Is it rocket science or nanophysics?) Try these for yourself: You can check the answers to these using the solutions at the end of the resource. Round to 2 decimal places: And, some problems: 1. How much would you pay for 1.8 kg apples if they cost $4.59 per kg? 2. A sheet of glass measures 650 mm by 455 mm. Calculate the area in m 2, correct to 3 decimal places. (Hint: change the mm measurements to metres first by dividing by 1000, then multiply.) 3. Calculate the tax on $ at 35 cents in the dollar. (Hint: change the 35 cents to dollars first and multiply.) 3
4 SIGNIFICANT FIGURES Significant Figures are different from Decimal places, although we may round using either of them. But significant figures can apply to whole numbers as well as decimals. Significant figures are the digits that are regarded as important when stating a number or measurement. All nonzero numbers are significant. 0 ( zero ), when at the end of a whole number or at the beginning of a decimal, becomes a place holder and is not counted as significant. An example of this might be: the crowd at a game of football is accurately counted as Do you think it is more likely that a commentator would say: the crowd today is thirtyeight thousand, five hundred and twentyone, or would they say: the crowd is nearly forty thousand? The forty thousand is a lot easier to say, and for the listener to understand has only 1 significant figure (the 4) and the 0s tell us its place value that it is in the ten thousands column. The accurate number (38 521) has 5 significant figures (ALL OF THEM!) and when we read or hear it we know that everyone in the crowd has been counted. However, zeros are significant when they are between two nonzero digits, such as 504, which has 3 significant figures. Another example: Round to 2 significant figures. As with Decimal Places, we can put a line to the right of the number we need to round at, so (the 0s are not significant, and as the 52 are the first 2 significant figures we are only interested in them). The 1 tells us to leave the 2 alone, so (is approximately, or roughly equal to) , correct to 2 significant figures. Here are some for you to try. You can check your answers from the back of the handout. Round each of the following to 3 significant figures: (Note the space between the 38 thousand, and the 521. We don t use commas any more and use a space instead.) 4
5 And some more questions: 1. According to the distance from the Earth to the Moon is km. Express this distance correct to 2 significant figures. 2. The diameter of a golf ball is given by as cm. Express this correct to 3 significant figures. 5
6 SCIENTIFIC NOTATION We need to return to our Decimal (Base 10) System. For Scientific Notation, we talk about powers of 10, and we can actually express every number in terms of a power of 10. This is because of the following: I m sure you recognise 10 2 as meaning 10 x 10, which is 100. (See how it lines up with the 100 column!) means 10 x 10 x 10 which is And so on to the left. To the right, 10 1 is just 10. If you continue the pattern of powers from the left to the right, you will see that the next power (for units) should be 0. This is right! (If you want more information about this, and negative powers, please refer to CONNECT: Powers: POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!) The good thing about having powers of 10 to act as our place value column headings is that it gives us an efficient method of expressing ANY number, no matter how large or how small. This is called Scientific Notation, or Standard Form. 6
7 Writing a number in Scientific Notation, or Standard Form For example, we may wish to write the distance of the Earth to the Moon, km, in a more efficient form. We see that the 3 is really 3 hundred thousand, and is in the column of We put a decimal point after the 3 and call our number x To check this result, you can multiply by 10 x 10 x 10 x 10 x 10 (so you would move the decimal point to the right 5 times). Most people use this method to get the number in Scientific Notation in the first place! So, you place a decimal point after the first nonzero digit, then work out how many times you would multiply by 10 (by moving the decimal point) until you get back to the original number. Second Example: Write the number km in Scientific Notation. (This is the diameter of the Sun, according to So, we put a decimal point after the first nonzero digit, which in this case is 1, to get 1.39 (we don t need the zeros on the end as they are just place holders and are not significant ). Now, to work out the power of 10, either look at the position of the first digit in the number the 1 it is in the 10 6 column or else, count how many places you need to move the decimal point to the right to get back to the original number (6). So, km is the same as 1.39 x 10 6 km. Decimal numbers (numbers that are between 0 and 1) will always have negative powers of 10 as their multiplier. Example: The thickness of a human hair can be as small as metres. To write this in Scientific Notation, again we can put the decimal point after the first nonzero digit, which is a 1. We can look at where the 1 lines up with our powers of 10 in the table above uh oh, our number is too small, but we can see it would be 105 if we continue the pattern of powers. The other method is to count the number of places we move the point to the left this time to make the original number, again it would be 5, but in the negative direction. So, m is 1.7 x 105 metres. Remember: Decimal numbers are expressed with negative powers of 10, but numbers larger than 1 are expressed with positive powers of 10. Some for you to try. You can check your answers at the end of this resource. 7
8 Write these numbers in Scientific Notation (Standard Form): And some problems: 1. The distance from the Earth to the Sun has been calculated as km. (source: Write this distance in Scientific Notation. 2. A large flea is approximately m long. Write this measurement in Scientific Notation. 3. Very large or very small? (a) 6.73 x (b) 1.89 x If you need help with any of the Maths covered in this resource (or any other Maths topics), you can make an appointment with Learning Development through Reception: phone (02) , or Level 3 (top floor), Building 11, or through your campus. 8
9 ANSWERS to PROBLEMS Decimal places (correct to 2 decimal places) (correct to 2 decimal places) (correct to 2 decimal places). In this situation, the 9 goes up to 10 but this means that we need to put the 5 up to the 6. It s like 59 going up to 60. Problems x 4.59 = Rounding this to 2 decimal places we would get But in Australia now, we would pay $ Change the length measurements to metres: 650 mm = m = 0.65 m 455 mm = m = m Area = 0.65 x m 2 = m m 2 (correct to 3 decimal places) 9
10 3. Tax = 0.35 x = So the tax to pay would be approximately $ (or, probably, for the TaxPerson, $5 539). Significant Figures (correct to 3 significant figures). Don t forget the 0s on the end to act as place value holders (correct to 3 significant figures) (correct to 3 significant figures) (correct to 3 significant figures). Some more questions: km km (correct to 2 significant figures) cm 4.27 cm (correct to 2 significant figures). 10
11 Scientific Notation = x = 4.21 x = x = 9.3 x 102 And, some problems: km = x 10 8 km. I would probably answer this by rounding, eg km 1.50 x 10 8 km m = 3.3 x 103 m. 3. (a) VERY LARGE!!! (b) VERY SMALL! 11
OPERATIONS: x and. x 10 10
CONNECT: Decimals OPERATIONS: x and To be able to perform the usual operations (+,, x and ) using decimals, we need to remember what decimals are. To review this, please refer to CONNECT: Fractions Fractions
More informationDECIMALS. Rounding Decimals Review and Multiplying Decimals. copyright amberpasillas2010. Rounding Review. Decimals are read as and
DECIMALS Rounding Decimals Review and Rounding Review Decimals are read as and 5 1 8 2 1, Thousands Hundreds Tens Ones Tenths Hundredths Read as 518 and 21 hundredths Thousandths Ten Thousandths 1 Rounding
More informationDecimal Notation ,000 10, Write a word name for the whole number. That is, the number to the left of the decimal point.
Decimal Notation Place Value Chart Hundreds Tens Ones Tenths Hundredths Thousandths Ten Thousandths 00 0 0 00,000 0, 000 Hundred Thousandths 00, 000 Millionths,000, 000 How to write a word name, given
More informationDECIMAL REVIEW. 2. Change to a fraction Notice that =.791 The zero in front of the decimal place is not needed.
DECIMAL REVIEW A. INTRODUCTION TO THE DECIMAL SYSTEM The Decimal System is another way of expressing a part of a whole number. A decimal is simply a fraction with a denominator of 10, 100, 1 000 or 10
More information12. [Place Value] A Q. What is the largest odd, 4 digit number, that contains the digits 0, 4, 5 and 7?
12. [Place Value] Skill 12.1 Understanding the place value of a digit in a number (1). When writing numbers the following is true: Each digit in a number occupies a special place or column. Larger numbers
More informationGrade 7  Chapter 1 Recall Prior Knowledge
MATH IN FOCUS Grade 7  Chapter 1 Recall Prior Knowledge REFRESH YOUR MEMORY! CHAPTER 1 Recall Prior Knowledge In order to be successful with the new information in Chapter 1, it is necessary to remember
More informationThe wavelength of infrared light is meters. The digits 3 and 7 are important but all the zeros are just place holders.
Section 6 2A: A common use of positive and negative exponents is writing numbers in scientific notation. In astronomy, the distance between 2 objects can be very large and the numbers often contain many
More informationUnit 7 : Decimals. Friendly Notes = 2 ones 5 tenths 6 hundredths 3 thousandths =
Unit 7 : Decimals Tenths, Hundredths, and Thousandths 1 one = 10 tenths 1 tenth = 10 hundredths 1 hundredth = 10 thousandths Friendly Notes 1. Write 42 tenths as a decimal. 42 tenths = 40 tenths + 2 tenths
More informationDECIMAL MODULE. I. Adding Decimals. II. Subtracting Decimals. III. Multiplying Decimals. IV. Dividing Decimals. BMR.
DECIMAL MODULE I. Adding Decimals II. Subtracting Decimals III. Multiplying Decimals IV. Dividing Decimals BMR.Decimals Page 1 I. Adding Decimals. Introduction: This is the first of four parts on working
More information2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division
Math Section 5. Dividing Decimals 5. Dividing Decimals Review from Section.: Quotients, Dividends, and Divisors. In the expression,, the number is called the dividend, is called the divisor, and is called
More informationDECIMALS. Place values. Converting decimals to fractions
DECIMALS Place values When working with decimals we need to insert a decimal point after the unit to separate the whole numbers from the fractions and extend the place values to include tenths, hundredths,
More informationPreAlgebra Lecture 6
PreAlgebra Lecture 6 Today we will discuss Decimals and Percentages. Outline: 1. Decimals 2. Ordering Decimals 3. Rounding Decimals 4. Adding and subtracting Decimals 5. Multiplying and Dividing Decimals
More informationCONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME!
CONNECT: Powers and logs POWERS, INDICES, EXPONENTS, LOGARITHMS THEY ARE ALL THE SAME! You may have come across the terms powers, indices, exponents and logarithms. But what do they mean? The terms power(s),
More informationActivity 21. Extending the place value system
2. DECIMAL NUMBERS 21 Extending the place value system 2 22 Is it a decimal point? 5 23 The size of decimal numbers 6 24 Scales with decimal numbers 7 25 Decimal accuracy 8 26 Rounding decimal numbers
More informationFROM THE SPECIFIC TO THE GENERAL
CONNECT: Algebra FROM THE SPECIFIC TO THE GENERAL How do you react when you see the word Algebra? Many people find the concept of Algebra difficult, so if you are one of them, please relax, as you have
More informationLesson 1 Order of Operations
Lesson 1 Order of Operations "Operations" means things like add, subtract, multiply, divide Student A solved the following problem: 177 x 2 = 20. Is he correct? Why or why not? Lesson 1 Order of Operations
More information1 3 7 5. 2 3 1 6. The pattern going to the right or the left from the decimal point is the same but there are two big differences:
Review of Place Values in Decimal Numbers A decimal number includes a decimal point and digit(s) to the right of the decimal point. Saying a decimal number aloud is very similar to saying a whole number
More informationNumber Skills for Public Health
Number Skills for Public Health Rounding, Percentages, Scientific Notation and Rates These notes are designed to help you understand and use some of the numerical skills that will be useful for your studies
More informationSimply Math. Everyday Math Skills NWT Literacy Council
Simply Math Everyday Math Skills 2009 NWT Literacy Council Acknowledgement The NWT Literacy Council gratefully acknowledges the financial assistance for this project from the Department of Education, Culture
More informationCHAPTER 4 DIMENSIONAL ANALYSIS
CHAPTER 4 DIMENSIONAL ANALYSIS 1. DIMENSIONAL ANALYSIS Dimensional analysis, which is also known as the factor label method or unit conversion method, is an extremely important tool in the field of chemistry.
More informationNumber: Number and Place Value with Reasoning
count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number Number: Number and Place Value with Reasoning +COUNTING Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count
More informationTrades Math Practice Test and Review
Trades Math Practice Test and Review This material is intended as a review only. To help prepare for the assessment, the following resources are also available:. online review material (free of charge)
More informationMathSphere MATHEMATICS. Equipment. Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions
MATHEMATICS Y6 Fractions 6365 Round decimals. Equivalence between decimals and fractions Paper, pencil, ruler Fraction cards Calculator Equipment MathSphere 6365 Round decimals. Equivalence between fractions
More informationis your answer, but you are asked to give the answer (correct to 2 decimal places). then the second number is increased by 1.
DECIMAL PLACES Sometimes you are required to give a shorter answer than the one which you have worked out. Example 1 3.68472 is your answer, but you are asked to give the answer correct to 2 decimal places
More informationStudent Outcomes. Lesson Notes. Classwork. Exercises 1 and 2 (3 minutes) Socratic Discussion (3 minutes)
Student Outcomes Students continue to practice working with very small and very large numbers expressed in scientific notation. Students read, write, and perform operations on numbers expressed in scientific
More informationChapter 3 Review Math 1030
Section A.1: Three Ways of Using Percentages Using percentages We can use percentages in three different ways: To express a fraction of something. For example, A total of 10, 000 newspaper employees, 2.6%
More informationFive daily lessons. Page 23. Page 25. Page 29. Pages 31
Unit 4 Fractions and decimals Five daily lessons Year 5 Spring term Unit Objectives Year 5 Order a set of fractions, such as 2, 2¾, 1¾, 1½, and position them on a number line. Relate fractions to division
More informationDECIMALS are special fractions whose denominators are powers of 10.
DECIMALS DECIMALS are special fractions whose denominators are powers of 10. Since decimals are special fractions, then all the rules we have already learned for fractions should work for decimals. The
More informationDecimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us
Decimals 1 Decimals are absolutely amazing We have only 10 symbols, yet can represent any number, large or small We use zero (0) as a place holder to allow us to do this 2 Some Older Number Systems 3 Can
More informationChapter 2 Formulas and Decimals
Chapter Formulas and Decimals Section A Rounding, Comparing, Adding and Subtracting Decimals Look at the following formulas. The first formula (P = A + B + C) is one we use to calculate perimeter of a
More informationDecimals Worksheets. The decimal point separates the whole numbers from the fractional part of a number.
Decimal Place Values The decimal point separates the whole numbers from the fractional part of a number. 8.09 In a whole number the decimal point is all the way to the right, even if it is not shown in
More informationRATIONAL NUMBERS CHAPTER
RATIONAL NUMBERS CHAPTER 70 CHAPTER RATIONAL NUMBERS Section. Recognizing, Reading, Writing and Simplifying Fractions What is a fraction? You have a circle. Cut it into two equal parts. Each part is called
More informationDIVISION OF DECIMALS. 1503 9. We then we multiply by the
Tallahassee Community College 0 DIVISION OF DECIMALS To divide 9, we write these fractions: reciprocal of the divisor 0 9. We then we multiply by the 0 67 67 = = 9 67 67 The decimal equivalent of is. 67.
More informationPAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE
PAYCHEX, INC. BASIC BUSINESS MATH TRAINING MODULE 1 Property of Paychex, Inc. Basic Business Math Table of Contents Overview...3 Objectives...3 Calculator...4 Basic Calculations...6 Order of Operation...9
More informationSolution: There are TWO square roots of 196, a positive number and a negative number. So, since and 14 2
5.7 Introduction to Square Roots The Square of a Number The number x is called the square of the number x. EX) 9 9 9 81, the number 81 is the square of the number 9. 4 4 4 16, the number 16 is the square
More informationFractions to decimals
Worksheet.4 Fractions and Decimals Section Fractions to decimals The most common method of converting fractions to decimals is to use a calculator. A fraction represents a division so is another way of
More informationUNIT 5 VOCABULARY: DECIMAL NUMBERS
º ESO Bilingüe Página UNIT 5 VOCABULARY: DECIMAL NUMBERS.. Decimal numbers Decimal numbers are used in situations in which we look for more precision than whole numbers provide. In order to do that, we
More information3.1.1 Decimals and Fractions
3.. Decimals and Fractions Learning Objective(s) Read and write numbers in decimal notation. 2 Write decimals as fractions. 3 Write fractions as decimals. Introduction In addition to fraction notation,
More informationSupporting your child with maths
Granby Primary School Year 5 & 6 Supporting your child with maths A handbook for year 5 & 6 parents H M Hopps 2016 G r a n b y P r i m a r y S c h o o l 1 P a g e Many parents want to help their children
More informationDecimal numbers. Tenths and hundredths. 2 Write the decimal number each arrow points to.
Decimal numbers Tenths and hundredths A decimal point separates whole numbers from decimal fractions 3896 3 tens (30) 9 9 tenths ( 0 ) 8 ones (8) 6 6 hundredths (00 ) 9 6 = 3896 for the Middle East PBA
More informationDecimals and other fractions
Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very
More information=
21 Decimals In most everyday applications, one encounters numbers written in decimal notation such as the price of a comodity, the Gross National Product, the diameter of an atom, etc. In this section,
More informationGap Closing. Decimal Computation. Junior / Intermediate Facilitator's Guide
Gap Closing Decimal Computation Junior / Intermediate Facilitator's Guide Module 8 Decimal Computation Diagnostic...5 Administer the diagnostic...5 Using diagnostic results to personalize interventions...5
More informationExponents. Exponents tell us how many times to multiply a base number by itself.
Exponents Exponents tell us how many times to multiply a base number by itself. Exponential form: 5 4 exponent base number Expanded form: 5 5 5 5 25 5 5 125 5 625 To use a calculator: put in the base number,
More informationCONNECT: Areas, Perimeters
CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a twodimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width
More informationGap Closing. Decimal Computation. Junior / Intermediate Student Book
Gap Closing Decimal Computation Junior / Intermediate Student Book Module 8 Decimal Computation Diagnostic...4 Adding Decimal Tenths or Hundredths...6 Adding Mixed Decimals...10 Subtracting Decimal Tenths
More informationMath. Rounding Decimals. Answers. 1) Round to the nearest tenth. 8.54 8.5. 2) Round to the nearest whole number. 99.59 100
1) Round to the nearest tenth. 8.54 8.5 2) Round to the nearest whole number. 99.59 100 3) Round to the nearest tenth. 310.286 310.3 4) Round to the nearest whole number. 6.4 6 5) Round to the nearest
More informationBetter Math Topic 1: Understanding Numbers Topic 1.1 The Decimal Number System and Place Value (Whole Numbers)
Key On screen content Narration voiceover Web links Activity Under the Activities heading of the online program Quiz Under the Activities heading of the online program Number/Numeral Systems Throughout
More informationRoman Numeral Table. Basic Calculations Review
Basic Calculations Review I. Okay. It has been a long time since we have had to even THINK about Roman numerals vs. Arabic numerals, right? So just to refresh, a Roman numeral looks like this XVI but an
More information1.4 Rounding. It doesn t matter if use the same cards again because you ll probably ask for a different degree of rounding.
1.4 Rounding Rounding to the nearest integer, or nearest 10, 100, etc. and decimal places (another way of saying nearest tenth, nearest hundredth, etc.) need to be clear before venturing into significant
More informationTo Multiply Decimals
4.3 Multiplying Decimals 4.3 OBJECTIVES 1. Multiply two or more decimals 2. Use multiplication of decimals to solve application problems 3. Multiply a decimal by a power of ten 4. Use multiplication by
More informationLearning new things and building basic skills
Math Review TABE Answer Key 2 Learning new things and building basic skills may be challenging for you, but they also can be very exciting. When you follow the guidelines for learning basic skills, you
More informationRevision Notes Adult Numeracy Level 1
Revision Notes Adult Numeracy Level 1 Numbers The number 5 703 428 has been entered into a table. It shows the value of each column. The 7 is in the hundred thousands column The 0 cannot be missed out
More informationUnit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems
Unit 5 Ratios and Proportional Relationships: Real World Ratio and Percent Problems The material in this unit crosses three strands The Number System (NS), Expressions and Equations (EE), and Ratios and
More informationPlace Value and Rounding
4.1 Place Value and Rounding 4.1 OBJECTIVES 1. Identify place value in a decimal fraction 2. Write a decimal in words 3. Write a decimal as a fraction or mixed number 4. Compare the size of several decimals
More informationMATH 20 EXTRA PRACTICE/ Name
MATH 20 EXTRA PRACTICE/4.14.3 Name Identify the digit with the given place value. 1) 132.835 thousandths 2) 0.28852 tenthousandths 3) 0.137325 tenths Write the decimal number that has the specified place
More informationOperations on Decimals
Operations on Decimals Addition and subtraction of decimals To add decimals, write the numbers so that the decimal points are on a vertical line. Add as you would with whole numbers. Then write the decimal
More informationLesson 8. Decimals. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 8 Decimals Objectives Understand conceptually what decimal notation means Be able to convert from decimals to mixed numbers and fractions Round
More informationC ONTENTS. Expressions and Formulae Chapters 18. Relationships Chapters 918
C ONTENTS Expressions and Formulae Chapters 18 1 2 3 4 5 6 7 8 Approximation and Estimation...................... 1 Working with Surds.............................. 6 Using Indices..................................
More informationNegative Exponents and Scientific Notation
3.2 Negative Exponents and Scientific Notation 3.2 OBJECTIVES. Evaluate expressions involving zero or a negative exponent 2. Simplify expressions involving zero or a negative exponent 3. Write a decimal
More informationMaths Area Approximate Learning objectives. Additive Reasoning 3 weeks Addition and subtraction. Number Sense 2 weeks Multiplication and division
Maths Area Approximate Learning objectives weeks Additive Reasoning 3 weeks Addition and subtraction add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar
More informationExploring Greater Numbers
1 Exploring Greater Numbers Compare numbers to one million. A bumblebee can flap its wings about 200 times per second. A dragonfly can flap its wings about 38 times per second. 1. Predict how many times
More informationHOSPITALITY Math Assessment Preparation Guide. Introduction Operations with Whole Numbers Operations with Integers 9
HOSPITALITY Math Assessment Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre at George
More informationChapter 4. Fractions, Decimals, Percent s Worksheets. Name: Class::
Chapter 4 Fractions, Decimals, Percent s Worksheets Name: Class:: Rounding Worksheet NAME: Thousands Hundreds Tens Units Decimal. Tenths Hundredths Thousandths Use the table provided to help you round
More information5 Decimal numbers. 1 Decimal numbers. 2 How to read decimal numbers.
5 Decimal numbers 1 Decimal numbers Decimal numbers such as 3.762 are used in situations in which we look for more precision than whole numbers provide. As with whole numbers, a digit in a decimal number
More informationcount up and down in tenths count up and down in hundredths
Number: Fractions (including Decimals and Percentages COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number
More informationYear 5 Mathematics Programme of Study Maths worksheets from mathsphere.co.uk MATHEMATICS. Programme of Study. Year 5 Number and Place Value
MATHEMATICS Programme of Study Year 5 Number and Place Value Here are the statutory requirements: Number and place value read, write, order and compare numbers to at least 1 000 000 and determine the value
More informationDivide Decimal Numbers
Divide Decimal Numbers Scrapbooking is a popular Focus on After this lesson, you will be able to φ use estimation to φ φ place a decimal point in a quotient divide decimal numbers with and without a calculator
More informationPlace Value of Whole Numbers
Chapter 1 Review of Basic Arithmetic 3 1.1 Place Value of Numbers and Rounding Numbers Place value is the value of a digit as determined by its position in a number, such as ones, tens, hundreds, etc.
More informationFigure 1. A typical Laboratory Thermometer graduated in C.
SIGNIFICANT FIGURES, EXPONENTS, AND SCIENTIFIC NOTATION 2004, 1990 by David A. Katz. All rights reserved. Permission for classroom use as long as the original copyright is included. 1. SIGNIFICANT FIGURES
More informationWeek Which fraction is equal to the decimal below? 0.6 A. 3 / 5 B. 4 / 5 C. 3 / 10 D. 2 / Round to the nearest hundred: 24,957 4.N.
Week 4 16. Which fraction is equal to the decimal below? 0.6 A. 3 / 5 B. 4 / 5 C. 3 / 10 D. 2 / 5 4.N.4 17. What is the area of the shape above? A. 18 cm 2 B. 22 cm 2 C. 21 cm 2 D. 20 cm 2 4.M.1 18. Round
More informationUnit 6 Number and Operations in Base Ten: Decimals
Unit 6 Number and Operations in Base Ten: Decimals Introduction Students will extend the place value system to decimals. They will apply their understanding of models for decimals and decimal notation,
More informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More information5 to 14 Revision / Consolidation Pack Level D
5 to 4 Two Week Revision Pack TeeJay Publishers April 998 Level D 5 to 4 Revision / Consolidation Pack Level D Like the elephant don t forget Unless specified by calculators should not be used Number Money
More informationNumber: Fractions (including Decimals and Percentages) Reasoning
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 COUNTING IN FRACTIONAL STEPS Pupils should count in fractions up to 10, starting from any number and using the1/2 and 2/4 equivalence on the number line (Non Statutory
More informationThousands Hundreds Tens Units Tenths Hundredths Thousandths
Decimals MTH 3 03a, MTH 3 03b, MTH 3 0a, MNU 30a, MNU 308a Place Value It is vital to understand place value in decimal fractions. The decimal point is always between the units (ones) and the tenths
More informationWarmUp Activity #4. Name Date Concept: Understanding Components of Scientific Notation
WarmUp Activity #4 Name Date Concept: Understanding Components of Scientific Notation Directions: The following activity is designed to review writing very large or very small numbers in a more precise
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationFractions and Decimals
FRACTIONS AND DECIMALS 9 Fractions and Decimals Chapter. INTRODUCTION You have learnt fractions and decimals in earlier classes. The study of fractions included proper, improper and mixed fractions as
More informationBasic Calculations and Percentages
Saturday Xtra XSheet: 1 Basic Calculations and Percentages Key Concepts In this session, we will focus on summarising what you need to know about:  Basic Calculations (revision of earlier work) o Scientific
More informationUnit 5 Length. Year 4. Five daily lessons. Autumn term Unit Objectives. Link Objectives
Unit 5 Length Five daily lessons Year 4 Autumn term Unit Objectives Year 4 Suggest suitable units and measuring equipment to Page 92 estimate or measure length. Use read and write standard metric units
More informationYear Five Maths Notes
Year Five Maths Notes NUMBER AND PLACE VALUE I can count forwards in steps of powers of 10 for any given number up to 1,000,000. I can count backwards insteps of powers of 10 for any given number up to
More informationSECTION 5.1 CONSTRUCTING DECIMALS
D E C I M A L R E P R E S E N T A T I O N S 5 SECTION 5.1 CONSTRUCTING DECIMALS We have all been concerned about the cost of an item when we shop or go out to eat. For example, a cheeseburger might cost
More informationIntroduction 6 National curriculum objectives 7
Contents Introduction 6 National curriculum objectives 7 Number Add/subtract Lesson Plan 1 Place value Code book 8 Lesson Plan 2 Counting Stepping stones 12 Lesson Plan 3 Negative numbers Fairground ride
More informationMath Help and Additional Practice Websites
Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade7 http://www.softschools.com/grades/6th_and_7th.jsp
More information2.2: Addition of Whole Numbers and Decimals. Objective: To review placevalue concepts and the use of the partialsums and columnaddition methods.
: Addition of Whole Numbers and Decimals Objective: To review placevalue concepts and the use of the partialsums and columnaddition methods. Math Starter Write these numbers in expanded notation on
More informationGrade 7/8 Math Circles October 7/8, Exponents and Roots  SOLUTIONS
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Grade 7/8 Math Circles October 7/8, 2014 Exponents and Roots  SOLUTIONS This file has all the missing
More information2016 Arizona State University Page 1 of 15
NAME: MATH REFRESHER ANSWER SHEET (Note: Write all answers on this sheet and the following graph page.) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
More informationDividing Whole Numbers by Decimals, Pathway 1
Dividing Whole Numbers by Decimals Pathway OPENENDED You will need materials for modelling decimals (e.g., Hundredths Grids (BLM 8) or base ten blocks) Takuma is using cans that hold 0. L to pour water
More informationScientific Notation. Section 71 Part 2
Scientific Notation Section 71 Part 2 Goals Goal To write numbers in scientific notation and standard form. To compare and order numbers using scientific notation. Vocabulary Scientific Notation Powers
More informationH.C.C.T.P. Highway Construction Careers Training Program. Entrance Exam. Study Guide
H.C.C.T.P. Highway Construction Careers Training Program Entrance Exam Study Guide Entrance Exam Study Guide How to use this study guide: This study guide is to prepare you for the math section on your
More informationDecimals. Lesson 1: Decimal Place Value decimal place values! September 24, Decimal Place Value Unit.notebook. What is a decimal?
Decimal Place Value Unit.notebook Lesson : Decimal Place Value Jul 22 7:57 PM Jul 23 :0 AM What is a decimal? Whole Number Place Value A decimal is used to separate the whole number part of a number from
More information2. Length, Area, and Volume
Name Date Class TEACHING RESOURCES BASIC SKILLS 2. In 1960, the scientific community decided to adopt a common system of measurement so communication among scientists would be easier. The system they agreed
More informationMultiplying & Dividing Decimals by 10, 100, 1000
Multiplying & Dividing Decimals by 10, 100, 1000 Overview The ability to multiply numbers which include decimals by powers of 10 (10, 100, 1000 etc.) is important for estimating calculations and for converting
More informationtroduction to Algebra
Chapter Five Decimals Section 5.1 Introduction to Decimals Like fractional notation, decimal notation is used to denote a part of a whole. Numbers written in decimal notation are called decimal numbers,
More informationJunior Cert Maths Notes Sample Paper 1 (Higher Level) Ronan Mulloy
Junior Cert Maths Notes Sample Paper 1 (Higher Level) by Ronan Mulloy Table of Contents Number Theory... 3 1. Conversions.... 3 2. Rounding Off... 4 3. Average Speed and Fuel Consumption... 7 4. Number
More informationWhat is rounding? Rounding is deciding which ten, hundred or thousand a number is closest to.
What is rounding? Rounding is deciding which ten, hundred or thousand a number is closest to. 1. Ask yourself What place am I rounding my number to? Nearest Ten? Nearest Hundred? Nearest Thousand? 2. Think
More informationThe gas can has a capacity of 4.17 gallons and weighs 3.4 pounds.
hundred million$ ten million$ million$ 00,000,000 0,000,000,000,000 00,000 0,000,000 00 0 0 0 0 0 0 0 0 0 Session 26 Decimal Fractions Explain the meaning of the values stated in the following sentence.
More informationSaxon Math Home School Edition. September 2008
Saxon Math Home School Edition September 2008 Saxon Math Home School Edition Lesson 4: Comparing Whole Lesson 5: Naming Whole Through Hundreds, Dollars and Cent Lesson 7: Writing and Comparing Through
More information