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InsightfulPenguin3718

How do you transform a decimal number into a fraction? And how to do the opposite?

Sarah G

Hi ! :) Let's start with the easiest: turning a decimal number into a fraction.

What’s better than an example to explain it to you! Consider 0.225. We want to transform it into a fraction. To do this, we can write that:

                                                           $$0.225 = 0.225/1$$

We agree that any number ÷ by 1 will not change the number (e.g.  5 = 5/1, 0.3 = 0.3 / 1 ). Okay, now we want to get rid of the comma in the numerator, because a fraction cannot have a point.

To get rid of the decimal point, we just have to multiply the numerator by 10, 100 or 1000 depending on how many digits there are after the decimal point. However, when dividing or multiplying the numerator of a fraction, it is imperative to do the same with the denominator and vice versa.

So, here, we have 3 decimal places. We will multiply the numerator by 1000 to remove the comma and, therefore, we will also multiply the denominator by 1000, which gives:

$$0.225 ∗ 100 = 225$$

Finally, if we ask, we will have to simplify the fraction to its maximum. To do this we will look for the GCD between the denominator and the numerator. Here the GCD is 25.

225 ÷ 251000 ÷ 25 = 940

So much for turning a decimal number into a fraction.

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Now, let's go the other way around: transforming a fraction into a decimal number. A little more complicated.

Let's take the same example, but let’s do the opposite. We want to find what 9/40 equals as a decimal number.  (Click on the photo to see it better)

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Hope that answers your question.

Good day