Sec. 5.1 Decimal Applications: Introduction to Decimals Learning Objectives: 1. Know the meaning of place value for a decimal number, and write decimals in words. 2. Write decimals in standard form. 3. Write decimals as fractions. 4. Compare decimals. 5. Round decimals to a given place value. 6. Key Vocabulary: decimals, standard form, < (less than), > (greater than), = (equal to), round the decimal part. 1. Know the meaning of place value for a decimal number, and write decimals in words 3 1 6 7 3 4 2. 1 3 2 5 1 4 Millionths Tenthousandths Hundredthousandths Hundredthousands thousandths hundredths tenths and ones tens hundreds thousands Ten-thousands Millions Steps for Writing (or Reading) a Decimal in Words 1. Write the whole number part in words. 2. Write and for the decimal point. 3. Write the decimal part in words as though it were a whole number following by the place value of the last digit. Example 1. Write each decimal number in words. 1. 3.098 2. 0.78 2. Write decimals in standard form Example 2. Write each decimal number in standard form. 1. Eleven and two hundredths _ 2. Forty-seven thousandths 1
3. Write decimals as fractions Rule for Changing a Terminating Decimal to a Fraction: 1. Write the digit to the left of the decimal point as the integer of the fraction. 2. Write the digits to the right of the decimal point as the numerator of the fraction. 3. The denominator is a 1 followed by as many zeros as there are decimal digits in the decimal. 4. Reduce the fraction. Example 3. Write each decimal as a fraction or a mixed number. Write your answer in simplest form. 1. 0.02 2. 11.004 4. Compare decimals To compare decimal lines up the decimal point, then compare corresponding digits, starting at the left until the two of the digits are difference. If necessary, added zeros. Example 4. Insert <, >, or = to form a true statement. 1. 0.2 0.5 2. 0.14 0.14000 3. 0.9 0. 999 5. Round decimals to a given place value Steps for Rounding Decimals to a Place Value to the Right of the Decimal Point 1. Underline the digit that needs to be rounded. (the given place value) 2. Locate the digit to the right, then a. If this digit is 5 or greater, add 1 to the digit in the given place value and delete all digits to its right. b. If this is less than 5, delete all digits to the right of the given place value. Example 5. Round each decimal to the given place value. 1. 0.39 to the nearest tenth 2. 0.585 to the nearest hundredth Example 6. Round each monetary amount to the nearest cent or dollar as indicated. 1. $0.058 to the nearest cent 2. $17.88 to the nearest dollar 2
Sec. 5.2 Adding and Subtracting Decimals Learning Objectives 1. Add or subtract decimals. 2. Evaluate expressions with decimal replacement values. 3. Simplify expressions containing decimals. 4. Solving problems that involve adding and subtracting decimals. 1. Add or subtract decimals Step of Adding Decimal Lines up the decimal point, then add hundredths, tenths, ones, tens and so on. Carrying if necessary. Step of subtracting Decimal Lines up the decimal point, attach any needed zeros so that both numbers have the same number of decimal digits and then subtract. Borrowing if necessary. Example 1. Add or subtract as indicated. 1. 0.32+ 0. 02 2. 8 7. 3 3. 5.2+ 0.358+ 21. 005 4. 9.08 3. 465 2. Evaluate expressions with decimal replacement values Example 2. Evaluate each expression x+ y z for x = 2.4, y= 3 and z = 0. 51 3
3. Simplify expressions containing decimals Example 3. Simplify by combining like terms. 1. 14.2x + 11.9 9.6x 15. 2 2. 8.96y 2.31 4.08y+ 9. 68 4. Solving problems that involve adding and subtracting decimals Example 4. Solve. 1. Recently, Allison went shopping and spent $18.92 at the bookstore, $68.03 at the grocery store, and $129.76 at a department store. What is the total amount of money Allison spent? 2. Find the perimeter of a rectangular lawn that measures 40.93 feet by 27.09 feet. 4
Sec. 5.3 Multiplying Decimals and Circumference of a Circle Learning Objectives 1. Multiply decimals. 2. Multiply by powers of 10. 3. Evaluate expressions with decimal replacement values. 4. Find the circumference of a circle. 5. Solve problems by multiplying decimals. 6. Key Vocabulary: π(pi), perimeter, circumference, diameter, and radius. 1. Multiply decimals Steps to multiply decimals: 1. Multiply the two decimal numbers as if they were whole numbers. 2. The number of decimal digits in the product is the sum of the number of decimal digits in the factors. Example 1. Multiply. 0.51 0. 0045 2. Multiply by powers of 10 To multiply a decimal number by 10, 100, 1000, or a higher power of 10 is to move the decimal point as many places to the right as there are zeros in the power of 10 being multiplied. Example 2. Multiply. 0.048 10000 To multiply a decimal number by 0.1, 0.01, 0.001, 0.0001 is to move the decimal point as many places to the left the same number of places as there are decimal places in the power of 10 being multiplied. Example 3. Multiply. 2.908 0.001 5
3. Evaluate expressions with decimal replacement values Example 4. Evaluate each expressions 3 y+ z for y = 0. 3 and z = 7. 3 4. Find the circumference of a circle radius Circumference, C = 2 πr (use when radius is given) or C = π d (use when diameter is given) diameter d r= 2 Example 5. Find the circumference of a circle with radius is 7 feet. Give the exact circumference and an approximation. Use 3.14 for π. Exact answer: Approximation answer: Example 6. Find the circumference of a circle with diameter is 16 inches. Give the exact 22 circumference and an approximation. Use for π. 7 Exact answer: Approximation answer: 6
5. Solve problems by multiplying decimals Example 7. Elaine is fertilizing her garden. She used 5.6 ounces of fertilizer per square yard. The garden measures 60.5 square yards. How much fertilizer does she need? 7
Sec. 5.4 Dividing Decimals Learning Objectives 1. Divide decimals. 2. Divide decimals by powers of 10. 3. Evaluate expressions with decimal replacement values. 4. Solve problems by dividing decimals. 1. Divide decimals Steps for Dividing a Decimal by a Whole Number: 1. Place the decimal point in the quotient directly above the decimal point in the dividend. 2. Divide as with whole numbers. Example 1. Divide. 26 7.826 Steps for Dividing a Decimal by a Decimal: 1. Move the decimal point in the divisor to the right until the divisor is a whole number. 2. Move the decimal point in the dividend to the right the same number of places as the decimal point was moved in step 1. 3. Divide. Place the decimal point in the quotient directly over the moved decimal point in the dividend. Example 2. Divide. 8.9 22.25 2. Divide decimals by powers of 10 To Dividing a Decimal number by 10, 100, 1000, or a higher power of 10 is to move the decimal point as many places to the left as there are zeros in the power of 10 being divided Example 3. Divide. 1.047 100 8
3. Evaluate expressions with decimal replacement values Example 4. Evaluate each expressions z y for y = 0. 3 and z = 1. 51 4. Solve problems by dividing decimals Example 5. The total cost of a loan is $ 231.75. How many monthly payments of $25.75 would it take to payoff the loan? 9
Sec. 5.5 Fractions, Decimals, and Order of Operations Learning Objectives 1. Write fractions as decimals. 2. Compare fractions and decimals. 3. Simplify expressions containing decimals and fractions using order of operations. 4. Solve area problems containing fractions and decimals. 5. Evaluate expressions given decimal replacement values. 1. Write fractions as decimals Steps for Writing Fraction a Decimal is to divide the numerator by the denominator. Example 1. Write each fraction as a decimal. 1 13 1. 2. 16 11 3. 7 1 8 2. Compare fractions and decimals Example 2. Insert <, >, or = to form a true statement. 5 7 0.72 10
Example 3. Write the numbers in order from smallest to largest. 15 2.15, 2.142, 7 3. Simplify expressions containing decimals and fractions using order of operations Example 4. Simplify each expression. 1. 0.1558 0.02 4. 45 2 2. ( 3.6) + 4.5 8. 7 11
4. Solve area problems containing fractions and decimals Example 5. Find the area of. Do not forget the units. 1. 46 ft. 36.5 ft. 2. 0.5 m 3 6 4 m 5. Evaluate expressions given decimal replacement values x Example 6. Evaluate each expressions + 2z for x = 2, y= 0. 5and z = 3. 6 y 12
Sec. 5.6 Equations Containing Decimals Learning Objectives 1. Solve Equations Containing Decimals 1. Solve Equations Containing Decimals Example 1. Solve each equation. 1. x + 0.8= 2. 5 2. 0.27y = 0. 81 3. 5 a + 3.6= 8a+ 12. 9 6.8 4x = 5x 13.7 4. ( ) 13
Sec. 5.7 Mean, Median, and Mode Learning Objectives 1. Find the mean of a list of numbers. 2. Find the median of a list of numbers. 3. Find the mode of a list of numbers. 4. Find the grade point average (GPA) or weighted mean. 4. Key Vocabulary: measures of central tendency, mean, median, mode, grade point average (GPA), weighted mean. 1. Find the mean of a list of numbers Definitions: Mean-is the sum of the items divided by the number of items. sum of items Mean= number of items Steps of finding the mean Add all numbers and divide by the number of the elements. Example 1. Find the mean of the following numbers: 1, 9, 27, 81, 243 and 3. Round the answer to the nearest hundredths. 2. Find the median of a list of numbers Definitions: Median is the middle number. If the number of items is odd, the median is the middle number. If the number of items is even, the median is the mean of the two middle numbers. Steps of finding the median: 1. Write numbers from the smallest to largest. 2. The median is the middle number. 3. If there is no middle number, then the median is the average of two middle numbers. Example 2. Find the median of the following numbers. 1. 1, 27, 8, 125, 64 2. 1, 3, 27, 81, 9, 243 14
3. Find the mode of a list of numbers Definitions: Mode is the numbers that occurs most often. It is possible for a set of numbers to have more than one mode or to have no mode. Steps of finding the Mode: 1. The mode is the number that occurs most often. 2. In the set, we can have more than one mode. 3. If there is no number that occurs most often, then the set has no mode. Example 3. Find the mode(s) of the following numbers if there is one. 1. 29, 25, 22, 25, 52, 8 2. 2, 8, 8, 1, 2, 8, 2 4. Find the grade point average (GPA) or weighted mean Steps of finding the grade point average (GPA ) or weighted mean 1. Compute points earn: points earned = credit hours weight of letter grade total points earned 2. Compute GPA: GPA = total credit hours Example 4. Find the GPA for a student taking 13 hours at Pierce College. Use the following for point values of the grades: A 4, B 3, C 2, D 1, F 0. If necessary, round the grade point average to the nearest hundredth. Course Credit Hours (CH) Grade Points earned PY102 3 A SO101 3 C BI101 4 B PE129 1 A HE107 2 B 15