1. PLACE VALUE. times smaller. The decimal point is the most important part of a Decimal Number.

Transcription

1 LESSON 5 1. PLACE VALUE When we write numbers, the position (or place ) of each number is important. As we move left, each position is 10 times bigger. As we move right, each position is 10 times smaller. The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. A tenth is 1 / 10 of a unit A hundredth is 1/100 of a unit A thousandth is 1 / 1000 of a unit The decimal point marks the end of the whole numbers. Digits on the left of the point are whole numbers Digits on the right of the point are decimal fractions (fractions of a whole number). Where there is no whole number, begin with a zero in the units position. Digits after the decimal point are usually read individually Examples: Twenty-seven point five is written 27.5 Nine point zero six is written 9.06 One hundred and one point zero zero two is written We can read the decimal number as one hundred twenty seven and five hundred seventy-eight thousandths. But in daily life, we usually read it as one hundred twenty seven point five seven eight. 1/5 IES UNIVERSIDAD LABORAL Mercedes López

2 Ordering decimals. Ordering decimals means putting them in order from smallest to largest or from largest to smallest. Line up the decimal points. Compare the digits in each column, starting on the left. Write down place value headings if it helps you. Below we are comparing and to see which is bigger. Both numbers have 0 units. So look in the tenths column. Both numbers have 4 tenths. So look in the hundredths column has 9 in the hundredths column whereas only has 5 in the hundredths column. (There is no need in this example to compare the thousandths column.) So is bigger than This video 1 shows you how to do it. Decimals can be indicated on the number line in between whole numbers. 0.5 and 1.65 are indicated on the figure below. How to Round Numbers Decide which is the last digit to keep Increase it by 1 if the next digit is 5 or more (this is called rounding up) Leave it the same if the next digit is less than 5 (this is called rounding down) You need to know if you are rounding to tenths, or hundredths, etc. Or maybe to so many decimal places. That tells you how much of the number will be left when you finish /5 IES UNIVERSIDAD LABORAL Mercedes López

3 Examples Because rounded to hundredths is 3.14 the next digit (1) is less than rounded to tenths is 1.3 the next digit (6) is 5 or more rounded to 3 decimal places is the next digit (5) is 5 or more Example Rounding to 2 decimal places. Jean used a calculator to work out some prices. The answers were recorded as and pence, so used two decimal places. To get the second decimal place right she looked at the third decimal place in each number to decide whether to round up or down. 2. OPERATIONS WITH DECIMALS. Adding and subtracting decimals Line up the decimal points and then add or subtract as normal as if the decimal point wasn t there. Don t forget to put the decimal point in your answer. Multiplying decimals. To multiply two decimal numbers, 3/5 IES UNIVERSIDAD LABORAL Mercedes López

4 Step 1 : Multiply the decimal numbers the same way as multiplication of whole numbers. Step 2 : The number of decimal places of the product (answer) is the sum of all decimal places of each number. Example : Evaluate Solution: 3. DIVIDING DECIMALS. If the dividend or divisor in a division are decimals, you change both numbers multiplying them by a power of ten, so that they become whole numbers. For instance: What is ? Solution: = = = 1800 (Multiply numerator and denominator by 100)= Try the following exercises: Exercise 1 2 Exercise 2: Jake had three lengths of wood, measuring 2.46m, 1.35m and 0.92m. What was their total length? Exercise 3: Sara cut 8.45m from a length of ribbon 16.70m long. What length of ribbon was left? Exercise 4: Jo bought 27 lengths of decking each 1.75m long. What was their total length? 2 4/5 IES UNIVERSIDAD LABORAL Mercedes López

5 Exercise 5: Talia worked for 23 hours at a rate of 6.35 an hour. How much was this altogether? Exercise 6: The cost of a meal for 17 people was , and they shared the amount equally. How much did each pay? Exercise 7: Tom bought 63.7m of fabric and cut it into 26 equal lengths. What was the length of each piece? Exercise 8: Angie used 16 litres of petrol for a journey of miles. How many miles was this per litre? Autoevaluation 3 (Level C) GLOSSARY Look for the following words in this dictionary 4 and copy them in your notebook. Tenth Hundredth Thousandth Increase Round /5 IES UNIVERSIDAD LABORAL Mercedes López