Convert Decimals to Fractions

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# Convert Decimals to Fractions - PowerPoint PPT Presentation

Convert Decimals to Fractions. Place Value Review. Tens Ones . Tenths Hundredths Thousandths Ten Thousandths. 15 . 7456. What I already know…. 0.5 = ½ 0.75 = ¾ 0.125 = 1 / 8

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## Convert Decimals to Fractions

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### Convert Decimals to Fractions

Place Value Review

Tens

Ones

.

Tenths

Hundredths

Thousandths

Ten Thousandths

15 . 7456

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.
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
• 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.
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?
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?
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?
• 0.4444444…
• 4/9
• 1.54545454….
• 153/99 = 1 54/99
• 0.36363636…
• 36/99 = 4/11