ACT Math : Decimals with Fractions

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #261 : Arithmetic

Convert this decimal to a fraction in reduced form:

Possible Answers:

Correct answer:

Explanation:

To figure out what fraction this decimal corresponds to, we have to get rid of the repeating part, otherwise we would be dealing with an infinite recursion and we don't have the tools to deal with that yet. Instead, we will set the decimal equal to  and multiply it by 10, and also multiply it by 100.

Notice that in  and  we have the same repeating decimal part. So if we subtract them, it disappears:

Now all that remains is to do the algebra.

 is our final answer.

Example Question #4 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of ?

Possible Answers:

Correct answer:

Explanation:

To find the fractional equivalent of a decimal, set the decimal as a fraction over , then multiply top and bottom by one power of  for each digit after the decimal. In this case, we have two digits after the decimal, so we multiply top and bottom by :

Now, start simplifying.

Since we cannot reduce further, .

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