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Math 81 Activity # 17 “Converting between Fractions and Decimals” Your Name: ___________________ Team Member #1__________________ Team Member #2.______________ Team Member #3__________________ Task 1: Convert a decimal to a fraction. Note: The Key is to read the decimal as you would write the decimal notation in words. Problem 1: Convert the decimal 0.6 to a Problem 2: Convert the decimal 4.75 to a fraction. fraction. Solution: 0.7 is read as seven-tenths, Solution: 4.75 is read as four and 7 and in fraction form it is . seventy-five hundredths, which refer 10 75 to the mixed number 4 . In simplest 7 Hence, 0.7 100 10 75 25 3 3 form, 4 4 4 . As a 100 25 4 4 3 19 19 fraction 4 , so 4.75 . 4 4 4 Problem 3: Convert the decimal 0.42 to a fraction. a) 0.42 is read as ____________________ b) Write it in fraction form _________ c) Can it be simplified? ________. If so, what is the fraction in simplest form: __________(Show your work below) d) Therefore, 0.42 Convert each of the following decimals to a fraction in simplest form. 1) 0.17 2) 0.785 3) 8.42 7 Problem 4: Convert the decimal 0.15 to a fraction 8 7 Solution: 0.15 is read as fifteen and seven eighths hundredths, and in fraction 8 form it is 7 127 15 8 8 Since the fraction bar representsdivision, we may rewrite it using the division symbol 100 100 127 100 8 127 1 8 100 127 800 Convert the following decimal to a fraction. 2 4) 0.16 3 Task 2: Convert a fraction to a decimal. Note: To convert a fraction to a decimal. The Key is to divide. Then, round the decimal to the indicated place value. 7 8 Problem 5:Convert the fraction to a Problem 6:Convert the fraction to 40 3 decimal. decimal. Round to the nearest hundredth. Solution: Solution: Since the fraction bar represents Again since the fraction bar represents 7 8 division, we have 7 40 . division, we have 8 3 . So we will take 5 40 3 So, we will take 7 divided by 40. divided by 6. Using long division, we Using long division, we have 40 7 , which have 3 8 , which the same is is the same as 40 7.000 2.666 3 8.000 0.175 6 40 7.000 20 40 18 300 20 28 0 18 200 20 200 18 0 2 7 Now rounding 2.666 to the nearest Hence, 0.175 40 8 hundredth, we get 2.67. Hence, 2.67 3 5 Problem 7: Convert the fraction 2 to a decimal. Round to the nearest 6 thousandths. Solution: Solution: 5 17 5 5 Method 1: Since 2 17 6 , using Method 2: Since 2 2 , using long 6 6 6 6 long division we will take 17 divided by 6. division we will take 5 divided by 6. 2.8333 0.8333 6 17.0000 6 5.0000 12 48 50 20 48 18 20 20 18 18 20 20 18 18 2 2 Now rounding 2.8333 to the nearest Now rounding 0.8333 to the nearest thousandth, we have 2.833 . Hence, thousandth, we have 0.833 . Hence, 5 5 5 2 2.833 2 2 2 0.8333 2.8333 6 6 6 Tip: When converting a fraction to a decimal with a denominator that is a multiple of 10 such as 10, 100, 1000, etc., division is not necessary. In other words, the decimal notation can be obtained by reading as you would write the fraction in words. 7 Example: Convert the fraction to a decimal. 100 7 Solution: is read as “seven hundredths”. In decimal form it is 0.07 . 100 Convert the following fractions to a decimal. Round to the nearest thousandth when necessary. 23 27 5) 6) 1000 4 5 7 7) 8) 4 12 9 Task 3: To identify the order relation between a decimal and a fraction. 5 Problem 6: Place the correct symbol, < or >, between the numbers and 0.312 . 16 Solution: 5 5 Convert to a decimal by dividing 0.3125 . 16 16 Note that 0.312 0.3120 . So comparing the two decimals, we have 0.3125 0.3120 5 Hence, 0.312 16 Place the correct symbol, <, =, or >, between the numbers. 9) 3.08_____3.082 10) 5.08_____5.80 7 5 11) _____0.583 12) _____0.2083 12 24 Convert each of the following decimals to a fraction in simplest form. 13) 0.36 14) 4.125 15) 0.270 16) 0.12 2 17) 0.025 18) 0.09 2 3 7 Convert each of the following fractions to a decimal. Round to the nearest hundredth. 2 7 19) 20) 13 6 5 75 21) 12 22) 6 1000