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Knowing how to move from one form of equivalent number to another can often be helpful to make calculations easier. In this lesson, learn how to represent a decimal as a fraction.

Steps for Solving the Problem

When we were younger, it seemed like the only limit to the number of different ways our teachers had for us to represent equivalent values was the number of days in the school year.

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Fractions, decimals, scientific notation, proportions, etc. However, it’s useful to be able to move from one form to another. For example, how many times have you moved back and forth between fractions and decimals when putting recipes together, since cups and teaspoons are in fractions (for example, ; cup, 1/3 cup and ; cup)? Making that conversion is simpler than you might think, and requires only some basic math skills.

First, let’s look at what decimals are. Decimals such as 0.7, 0.25, and even 6.41 are ways to represent values that are not whole numbers.

Because the world doesn’t always exist in whole numbers (for example, most people are not either 5.0 or 6.0 feet tall), this is a normal everyday requirement in dealing with numbers.The number of digits you find in the decimal to the right of the decimal point tells you how specific the decimal is. One decimal point (0.7) is tenths, two decimal points (0.25) is hundredths, three decimal points (0.

832) is thousandths, and so on (ten-thousandths, hundred-thousandths, millionths, etc.). Knowing this becomes important when converting decimals to fractions, as we will see.

In the case of 0.25, since we know the decimal represents hundredths, we can say it is 25 hundredths. Fraction-wise, this looks like:

25 hundreths


However, the process can be made even simpler. Remember, the goal here is to come up with the fraction that is equal to the decimal value.

Three other nuggets of information are important here:

  1. Any number divided by one is equal to itself (for example, 0.25/1 = .25).
  2. Any number divided by itself equals 1 (for example, 735 / 735 = 1).
  3. Any number multiplied by one is equal to itself (for example, 17 x (735/735) = 17).

Putting these facts to work is one way to convert decimals to fractions.Now do the following:1. Write the decimal as a fraction by putting the decimal value as numerator (top) and 1 as the denominator (bottom).


point 25 over 1


2. Multiply by a form of 1, with a multiple of 10 that has as many zeroes as there are places to the right of the decimal point (for example, for 3 decimal points, use 1000/1000, for 5 decimal places, 100,000/100,000).


Converting point 25 to a fraction


3. Reduce the fraction, if necessary.

Solution

So .

25 as a fraction is equal to ;.

Reduction of fraction


Checking Your Work

Basic understandings of numbers can help us make sure we have made an accurate conversion.Most important is probably a number line between zero and 1 with fractions and decimals on it.


Fractions and Decimals


Keep in mind that fractions are simply division problems (for example, 4/11 = four divided by eleven). Depending on your available time and comfort level, you can either work the problem out by hand or use a calculator. The value you get should equal the original decimal. In the 0.25 example, 1/4 = 0.25, as does 25/100 = 0.25.

1 fourth equals point 25


25 over 100 equals point 25


To convert decimals to fractions, simply turn the decimal into a fraction by putting it over one, multiply it by 1 (in the form of tenths, hundredths, thousandths, depending on how many decimal places), and simplify the resulting fraction if possible, or necessary.

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