Which is smaller, -1/3 or -0.3 Step by Step

Step by step

The question

Question: which is smaller, −1/3 or −0.3?

−13 or −0.3

1 Write it as a decimal

To compare, we write every number the same way: as a decimal.

The bottom 3 does not go into 10, 100 or 1000.

So we divide: 1 divided by 3, one digit at a time.

= −13 = −1 ÷ 3 = −0.333…

10 divided by 3 is 3, with 1 left.

1 left again: the 3 repeats for ever.

So −1/3 is −0.333….

10 ÷ 3 = 3, 1 left: the 3 repeats

Careful!

−1/3 is not −0.3.

Its 3s go on for ever, so it is a bit further below 0 than −0.3.

Careful: not −13 = −0.3 ✗

2 Same number of digits

Zeros at the end of a decimal do not change it: −0.3 is the same as −0.300.

A repeating decimal goes on for ever, so we can write as many of its digits as we need.

So we give every number 3 digits after the point.

= −0.333…, −0.300

3 Compare

Negative numbers are below 0.

333 > 300, so −0.333… is further below 0.

Further below 0 means smaller.

= −0.333… < −0.300

333 > 300: further below 0

4 Write the answer

Now with the numbers as they were given: −1/3 < −0.3.

So −1/3 is smaller.

= −13 < −0.3

5 Check

Let's check on a number line.

Smaller numbers are further to the left.

We put a dot for each number.

From left to right: −1/3, −0.3.

The same order.

So the answer is right!

left to right: same order

Let's look back.

First: write it as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.

Answer