Which is smaller, -0.2 or -1/4 Step by Step

Step by step

The question

Question: which is smaller, −0.2 or −1/4?

−0.2 or −14

1 Write it as a decimal

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

A decimal is tenths, hundredths or thousandths.

4 times 25 is 100.

So we multiply the top and the bottom by 25.

25 hundredths is 0.25.

The minus sign stays in front: −0.25.

= −14 = −1 × 254 × 25 = −25100 = −0.25

2 Same number of digits

Zeros at the end of a decimal do not change it: −0.2 is the same as −0.20.

So we give every number 2 digits after the point.

= −0.20, −0.25

3 Compare

Negative numbers are below 0.

25 > 20, so −0.25 is further below 0.

Further below 0 means smaller.

= −0.25 < −0.20

25 > 20: further below 0

Careful!

0.25 is more than 0.2.

But −0.25 is further below 0, so it is smaller.

Careful: not −0.25 > −0.2 ✗

4 Write the answer

Now with the numbers as they were given: −1/4 < −0.2.

So −1/4 is smaller.

= −14 < −0.2

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: −1/4, −0.2.

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