Fractions and Decimals in Order

Practically always, GED® Math includes tasks that ask you to put fractions and decimals in the correct order.

This sort of task is testing your knowledge of the order of operations in fractions and decimals.

First, place the following numbers in order, starting with the least to the greatest.

\(\frac{1}{4}\); \(0.5\); \(\frac{3}{8}\); and \(0.9\)

When we look at the given numbers, we see that some of these numbers are fractions, while others are decimals.

We know that it’s not so easy to compare fractions and decimals. So we can make our lives easier if we take all these fractions to convert them first into decimals. Then, we’ll end up with a lot of decimals that are easier to compare.

For this problem, we can use a calculator.

Step 1: Take each of these fractions and convert them into decimals.

So here we’ve got the fraction \(1\) over \(4\), and we want to convert it into a decimal.

So we will take our numerator and divide it by our denominator. So a \(1\) (one) divided by four \((4)\).

Well, when dividing \(1\) (one) by four \((4)\), we’ll get the \(0.25\) decimal. Fine.

Now, how about the next number, \(0.5\,?\)

Well, this already in the decimal form. We can leave this number as it is. What about the next one? \(\frac{3}{8}\) is a fraction. We must convert this number to decimal as well.

We’ll be taking our numerator \((3)\) and divide it by our denominator \((8)\). So we’re taking three \((3)\) divided by \((8)\) eight.

We use our calculator to have it in decimal form as well. Now, there is one more decimal \((0.9)\).

So now, we have of the numbers in decimal form, and that makes it quite easy to compare our decimals. Plot the numbers on the number line. We’re making our number line like this.

Fine. Now let’s go and plot each of the decimals on that number line and compare them.

Fine. So now, we’ve made this task rather easy using our number line. The number leftmost is the smallest number, while the rightmost one is the largest number.

On our number line, when we’ll be moving from left to right, the numbers will be getting bigger.

So now, we’ve placed our numbers in the least to greatest order (left to right), but initially, not all our numbers were decimals. Some began as fractions. So what we now need to do is take these decimals again and start converting them back to get fractions.

So now, we can simply rewrite it again and come up with the correct answer. We take the numbers and place them in the right order, from least to greatest.

Video Summary and Quiz

1. Between which pair of decimals should \(\frac{3}{8}\) be placed on a number line?

Question 1 of 2

2. Between which pair of decimals should \(\frac{1}{4}\) be placed on a number line?

Question 2 of 2


Next Lesson: Ratios


Last Updated on April 12, 2021.

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