Convert Decimals to Fractions Tens Ones Tenths Hundredths

Convert Decimals to Fractions

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

What I already know… 0. 5 = ½ 0. 75 = ¾ 0. 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.

Always REDUCE your fractions!

Convert the following terminating decimals to fractions. 1. 0. 4 1. 4/ 10 2. Reduces to 2/5 2. 1. 86 1. 1 and 86/100 2. Reduces to 1 43/50 3. 0. 795 1. 795/ 1000 2. Reduces to 159/200

What about nonterminating decimals? • How do you convert 0. 11111…. 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. 11111… to a fraction § How many digits are repeating? § 1 digit repeats § Place the repeating digit over that many 9 s. § 1/9 § Reduce, if possible. § This means that the fraction 1/9 is equal to 0. 111111… § With your calculator, divide 1 by 9. What do you get?

Try the steps again: § Convert 0. 135135135… to a fraction. § How may digits are repeating? § 3 digits repeat. § Place the repeating digits over that many 9 s. § 135/ 999 § Reduce if possible. § Divide the numerator and denominator by 9. § This means that the fraction 135/999 which reduces to 15/111 is 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. 7878… to a fraction. § How many digits are repeating. § 2 digits repeat. § Place the repeating digits over that many 9 s. § 78/ 99 § Reduce if possible. § Divide the numerator and denominator by 3. § This means that the fraction 4 78/99 reduces to 4 26/33 is equal to 4. 7878… § With your calculator, divide 78 by 99. What do you get? § Divide 26 by 33. What do you get?

Your turn. Change the following repeating decimals to fractions. 1. 0. 4444444… 1. 4/ 9 2. 1. 5454…. 1. 153/ 54/ = 1 99 99 3. 0. 3636… 1. 36/ 4/ = 99 11