ACT Math : How to find the fractional equivalent of a decimal

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #3 : Decimals

What is  equivalent to?

Possible Answers:

Correct answer:

Explanation:

We need to convert  into a fraction.

To do this, write down 

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

Now, simplify the fraction.

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

A tub of food contains  pounds of vegetables,  pounds of lard, and  pounds of sausage.  What is its total weight as an improper fraction?

Possible Answers:

Correct answer:

Explanation:

To begin with, it is easiest just to add these decimals together using your calculator:

Now, this is the same thing as:

We can rewrite this:

To find this, you need to give the two numbers a common denominator:

This is your answer.

Example Question #22 : Decimals

What is the fractional equivalent of ?

Possible Answers:

Correct answer:

Explanation:

In decimal form  is said 33 hundredths.

This is equal to

.

This fraction cannot be reduced any further therefore it is in its final answer form.

Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

Write 0.45 as a fraction.

Possible Answers:

Correct answer:

Explanation:

.45 is equivalent to 45 out of 100, or .

Divide both the numerator and denominator by 5 to simplify the fraction: 

Example Question #2 : How To Find The Fractional Equivalent Of A Decimal

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 #3 : 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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