Transforming Terminating Decimals to Fractions and Vice Versa – Practice Problems

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In real life it's often necessary to transform fractions into decimals or the other way round. Have you ever wondered why $0.25 is called a 'quarter?' Maybe you also came across a recipe where some measurements were given in fractions while others appeared in decimals.

When writing rational numbers as fractions or decimals, you can use two strategies, depending if you want to transform decimals into fractions or fractions into decimals.

Fractions are like unsolved division problems. Instead of ⅛, you can also write 1÷8, which you can solve in long division. Since your solution will be less than 1, write 0 above the division bar, include the decimal point, then add as many zeros to the dividend as you might need. Then start dividing as you're used to. Many simple fractions can be turned into decimals in only a few steps. Whenever you have 0 as a remainder, you are finished. Decimals that have only a few digits after the decimal point are called terminating decimals. There are fractions, such as ⅓, or 1÷3, however, that will never have 0 as a remainder and will go on forever with repeating digits. These are called repeating decimals.

For transforming terminating decimals into fractions you look at the length of your decimal repectively, to which place after the decimal point it goes to. 0.75, for example, goes to the hundreths place, so you can rewrite this number as 75 over 100. Guess how a decimal that goes to the thousandths place will be transformed into a fraction? Right, by rewriting this number with all digits after the decimal point over 1000.

Through the use of an everyday situation, this video will provide you with all you need to know about transforming fractions into terminating decimals and vice versa, including how to use long division for solutions that are less than 1.

Apply and extend previous understandings of operations with fractions. CCSS.MATH.CONTENT.7.NS.A.1

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Exercises in this Practice Problem
Write the decimals of the recipe as fractions.
Find the correct decimals for each fraction.
Convert each fraction into a decimal.
Identify where Sue succeeded in converting decimals into fractions.
Decide if the given numbers are fractions or decimals.
Find the numbers that represent the same value.