Comparing rational numbers

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Rational numbers can be written as fractions or decimals. For example, the following numbers are all rational:

3.4

–

2.25

–

0.1

Look at each rational number on a number line. Notice that the negative numbers are to the left of zero and the positive numbers are to the right of zero. The farther right you go, the greater the value.

How do you compare rational numbers?

When you compare rational numbers, it often helps to use a number line.

It can also help to write both numbers in the same form. You can write them both as fractions or as decimals. If the numbers are fractions, you can write them to have a

common denominator

to make them easier to compare.

Example 1

Let's try it! Compare 0.2 and

–

0.4

Since 0.2 is positive and

–

0.4

is negative, 0.2 is greater than

–

0.4

The number 0.2 is farther right on the number line.

So,

0.2

–

0.4

Example 2

Let's try another example. Compare

–

and

–

Since

–

and

–

have unlike denominators, rewrite them to have common denominators. You can use a denominator of 15.

–

Now you can compare the numbers.

Since

–

is farther right on the number line,

–

is greater than

–

So,

–

Example 3

Let's try one more example. Compare

and 1.85.

First, write both numbers as

decimals

Since

The number

can be written as the decimal 1.8.

Now, compare 1.8 and 1.85.

1.8

1.85

So,

1.85

Try some practice problems!

Compare rational numbers

How do you order rational numbers?

You can order rational numbers using what you know about comparing rational numbers.

Let's try an example. Put these rational numbers in order from least to greatest:

1.9,

–

2.32,

First, find the smallest number. Since negative numbers are always less than positive numbers,

–

is the smallest number.

Now, you are left with three positive numbers. Look at the whole number parts. Since 1 is less than 2, 1.9 comes next.

Last, look at the remaining numbers. To compare 2.32 and

write both numbers in the same form. Write

as a decimal.

2.3

Since 2.3 is less than 2.32,

comes next.

That leaves 2.32 as the largest number.

So, these are the rational numbers in order from least to greatest:

–

1.9,

2.32

Try some practice problems!

Put rational numbers in order

Skills

Compare rational numbers Put rational numbers in order

Videos

Compare rational numbers

Put rational numbers in order

Lessons

Comparing fractions

Comparing decimals

How do you compare rational numbers?

Example 1

Example 2

Example 3

Try some practice problems!

How do you order rational numbers?

Try some practice problems!

Related

Skills

Videos

Lessons