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

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.

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.

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.

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.

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, .

To convert this decimal to a fraction, rewrite over .

In the numerator, move the decimal place in two places to the right. Then add two zeros after the one in the denominator.

The answer is .

Divide by one.

Move the decimal place on the numerator 4 units to the right. Add as many zeros as placeholders for the denominator as many times as the decimal has moved. In other words multiply the numerator and denominator by 10000.

The correct answer is:

First simplify .

Since has a decimal 3 places from the right, divide this number by , and move the numerator decimal 3 places to the right. As a result:

This fraction can be reduced fully by using common factors. Simplify.