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Convert Decimals to Fractions

Convert Decimals to Fractions

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Convert Decimals to Fractions

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  1. Convert Decimals to Fractions

  2. Place Value Review Tens Ones . Tenths Hundredths Thousandths Ten Thousandths 15 . 7456

  3. What I already know… 0.5 = ½ 0.75 = ¾0.125 = 1/8 Use the place value of the last digit to determine the denominator. Drop the decimal and use that number as the numerator. • In the decimal 0.5 the “5” is in the tenths place so the denominator will be “10.” • The numerator will be 5. So the fraction is 5/10 which reduces to ½. • In the decimal 0.75 the last digit is in the hundredths place so the denominator will be “100.” • The numerator will be 75. So the fraction is 75/100 which reduces to ¾. • In the decimal 0.125 the last digit is in the thousandths place so the denominator will be “1000.” • The numerator will be 125. So the fraction is 125/1000 which reduces to 1/8.

  4. Always REDUCE your fractions!

  5. Convert the following terminating decimals to fractions. • 0.4 • 4/10 • Reduces to 2/5 • 1.86 • 1 and 86/100 • Reduces to 1 43/50 • 0.795 • 795/1000 • Reduces to 159/200

  6. What about non-terminating decimals? • How do you convert 0.1111111111….to a fraction? • We are told that repeating decimals are rational numbers. • However, to be a rational number it must be able to be written as a fraction of a/b.

  7. Steps to change a non-terminating decimal to a fraction: • Convert 0.111111111… to a decimal • How many digits are repeating? • 1 digit repeats • Place the repeating digit over that many 9s. • 1/9 • Reduce, if possible. • This means that the fraction 1/9is equal to 0.111111… • With your calculator, divide 1 by 9. What do you get?

  8. Try the steps again: • Convert 0.135135135… to a decimal. • How may digits are repeating? • 3 digits repeat. • Place the repeating digitsover that many 9s. • 135/999 • Reduce if possible. • Divide the numerator and denominator by 9. • This means that the fraction 135/999 which reduces to15/111is equal to 0.135135135… • With your calculator, divide 135 by 999. What do you get? • Divide 15 by 111. What do you get?

  9. One more time together: • Convert 4.78787878… to a decimal. • How many digits are repeating. • 2 digits repeat. • Place the repeating digitsover that many 9s. • 78/99 • Reduce if possible. • Divide the numerator and denominator by 3. • This means that the fraction 4 78/99 reduces to 4 26/33is equal to 4.7878… • With your calculator, divide 78 by 99. What do you get? • Divide 26 by 33. What do you get?

  10. Your turn.Change the following repeating decimals to fractions. • 0.4444444… • 4/9 • 1.54545454…. • 153/99 = 1 54/99 • 0.36363636… • 36/99 = 4/11