Compare -2 1/4 and -2.3 Step by Step

Step by step

The question

Question: compare −2 and 1/4 and −2.3.

−214 and −2.3

1 Write it as a decimal

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

The minus is in front of the whole number.

2 and 1/4 means 2 plus 1/4.

= −214 = −(2 + 14) = −(2 + 0.25) = −2.25

4 times 25 is 100, so we multiply the top and the bottom by 25.

1/4 is 25 hundredths: 0.25.

So −2 and 1/4 is −2.25.

1 × 254 × 25 = 25100 = 0.25

Careful!

The 1 and the 4 are a fraction, not digits after the point.

1/4 is 0.25.

Careful: not −214 = −2.14 ✗

2 Same number of digits

Zeros at the end of a decimal do not change it: −2.3 is the same as −2.30.

So we give every number 2 digits after the point.

= −2.25, −2.30

3 Compare

Negative numbers are below 0.

230 > 225, so −2.30 is further below 0.

Further below 0 means smaller.

= −2.30 < −2.25

230 > 225: further below 0

4 Write the answer

Now with the numbers as they were given: −2 and 1/4 > −2.3.

−2 and 1/4 is greater than −2.3.

= −214 > −2.3

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: −2.3, −2 and 1/4.

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