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1 Lesson 2.1.2 Converting Terminating Decimals to Fractions Converting Terminating Decimals to Fractions

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2 Lesson 2.1.2 Converting Terminating Decimals to Fractions California Standard: Number Sense 1.5 Know that every rational number is either a terminating or a repeating decimal and be able to convert terminating decimals into reduced fractions. What it means for you: Key Words: You’ll see how to change terminating decimals into fractions that have the same value. fraction decimal terminating

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3 Lesson 2.1.2 Converting Terminating Decimals to Fractions This Lesson is a bit like the opposite of the last Lesson — you’ll be taking decimals and finding their equivalent fractions. This is how you can show that they’re definitely rational numbers. 0.5 1 2 0.125 1 8

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4 Decimals Can Be Turned into Fractions Lesson 2.1.2 Converting Terminating Decimals to Fractions If you read decimals using the place-value system, then it’s more straightforward to convert them into fractions. 0.15 is said “fifteen-hundredths,” so it turns into the fraction. 15 100

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5 Lesson 2.1.2 Converting Terminating Decimals to Fractions You need to remember the value of each position after the decimal point: 0.1234 tenths hundredthsthousandths ten-thousandths decimal point

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6 Then when you are reading a decimal number, look at the position of the last digit. Lesson 2.1.2 Converting Terminating Decimals to Fractions 0.01 is one-hundredth, which is the fraction. 1 100 0.1 is one-tenth, which is the fraction. 1 10

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7 Example 1 Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Solution Convert 0.27 into a fraction. 0.27 is twenty-seven hundredths, so it is. 27 100 0.27 is twenty-seven hundredths,

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8 Example 2 Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Solution Convert 0.3497 into a fraction. 0.3497 is 3497 ten-thousandths, so it is. 3497 10,000 0.3497 is 3497 ten-thousandths,

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9 Guided Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Convert the decimals in Exercises 1–12 into fractions without using a calculator. 1. 0.12. 0.233. 0.17 4. –0.875. 0.76. 0.35 7. 0.1748. –0.3649. 0.127 10. 0.982711. 0.521212. –0.4454 1 10 23 100 17 100 –87 100 7 10 35 100 174 1000 127 1000 –364 1000 9827 10,000 5212 10,000 –4454 10,000

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10 When you convert decimals to fractions this way, you’ll often get fractions that aren’t in their simplest form. Some Fractions Can Be Made Simpler Lesson 2.1.2 Converting Terminating Decimals to Fractions If an answer is a fraction, you should usually give it in its simplest form. could be written more simply as 5 10 1 2 could be written more simply as 75 100 3 4

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11 This is how to reduce a fraction to its simplest form: Lesson 2.1.2 Converting Terminating Decimals to Fractions 1.Find the biggest number that will divide into both the numerator and the denominator without leaving any remainder. 2.Then divide both the numerator and the denominator by the GCF. This number is called the greatest common factor, or GCF. If the greatest common factor is 1 then the fraction is already in its simplest form — you can’t simplify it any more.

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12 0.12 is twelve hundredths. Example 3 Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Solution Convert 0.12 into a fraction. As a fraction it is. 12 100 The factors of 12 are 1, 2, 3, 4, 6, and 12. The biggest of these that also divides into 100 leaving no remainder is 4. Divide both the numerator and denominator by 4. So the greatest common factor of 12 and 100 is 4. 0.12 as a fraction in its simplest form is. 3 25 12 ÷ 4 100 ÷ 4 3 25 =

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13 Example 4 Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Solution Convert 0.7 into a fraction. 0.7 is seven tenths. As a fraction it is. 7 10 The greatest common factor of 7 and 10 is 1, so this fraction is already in its simplest form.

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14 Guided Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Convert the decimals in Exercises 13–20 into fractions and then simplify them if possible. 13. 0.2514. 0.65 15. –0.0216. 0.256 17. 0.017518. –0.84 19. 0.26720. 0.866 1 4 13 20 –1 50 –21 25 32 125 7 400 267 1000 433 500

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15 Guided Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions 21. Priscilla measures a paper clip. She decides that it is six-eighths of an inch long. Otis measures the same paper clip with a different ruler and says it is twelve-sixteenths of an inch long. How can their different answers be explained? is a simpler form of. Both answers are the same. 6 8 12 16

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Decimals Greater Than 1 Become Improper Fractions Lesson 2.1.2 Converting Terminating Decimals to Fractions When you convert a decimal number greater than 1 into a fraction it’s probably easier to change it into a mixed number first. Then you can change the mixed number into an improper fraction. 1.5 1 2 1 3 2

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17 Example 5 Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions 7 10 Convert 0.7 first — this becomes. Add on the 13. The result can be written as 13. 7 10 A mixed number. Solution Convert 13.7 into a fraction. So add to this: 13 whole units are equivalent to. 13 1 10 = 130 10 13 1 10 + = + = 7 10 130 10 7 137 10 7 Now turn 13 into an improper fraction. 7 10

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18 Guided Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Convert the decimals given in Exercises 22–33 into fractions without using a calculator. 22. 4.323. –1.0324. 15.98 25. –1.726. 9.727. –4.5 28. 12.90429. –13.14230. –8.217 31. 0.362732. 1.802833. 4.1234 43 10 –103 100 799 50 –17 10 97 10 –9 2 1613 25 –8217 1000 –6571 500 3627 10,000 4507 2500 20,617 5000

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19 Independent Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Convert the decimals given in Exercises 1–10 into fractions without using a calculator. 1. 0.32. 0.2 3. 0.44. 0.30 5. 0.266. 0.18 7. –0.348. –1.34 9. 0.23410. 2.234 3 10 117 100 1 5 3 10 1117 500 2 5 13 50 9 –17 50 –67 50

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20 Independent Practice Solution follows… Lesson 2.1.2 Converting Terminating Decimals to Fractions Convert the decimals given in Exercises 11–20 into fractions without using a calculator. 11. 9.14012. 3.655 13. –0.12114. –0.655 15. –10.76016. 5.001 17. 0.298518. 2.3222 19. –9.345220. –0.2400 457 50 –6 25 731 200 –121 1000 –131 200 –269 25 5001 1000 597 2000 11,611 5000 –23,363 2500

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21 Round Up Lesson 2.1.2 Converting Terminating Decimals to Fractions The important thing when converting a decimal to a fraction is to think about the place value of the last digit. Then read the decimal and turn it into a fraction. If the decimal is greater than 1, ignore the whole number until you get the decimal part figured out. Take your time, do each step carefully, and you should be OK.

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