Order 0.125, 1/10, 0.15, -1/8 from smallest to largest Step by Step

Step by step

The question

Question: put 0.125, 1/10, 0.15, −1/8 in order, from smallest to largest.

0.125, 110, 0.15, −18

1 Write each as a decimal

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

1 tenths is 0.1.

So 1/10 is 0.1.

= 110 = 0.1

8 times 125 is 1000.

So we multiply the top and the bottom by 125.

125 thousandths is 0.125.

The minus sign stays in front: −0.125.

= −18 = −1 × 1258 × 125 = −1251000 = −0.125

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.1 is the same as 0.100.

So we give every number 3 digits after the point.

= 0.125, 0.100, 0.150, −0.125

3 Compare

Now they all have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 100 < 125 < 150.

= 0.100 < 0.125 < 0.150

100 < 125 < 150

Careful!

More digits does not mean bigger.

Compare 0.125 with 0.150.

Careful: not 0.125 > 0.15 ✗

Negative numbers are smaller than every positive number.

So they come first.

= −0.125 < 0.100 < 0.125 < 0.150

4 Write the answer

Now we write the numbers as they were given, in the same order: −1/8, 1/10, 0.125, 0.15.

= −18 < 110 < 0.125 < 0.15

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: −1/8, 1/10, 0.125, 0.15.

The same order.

So the answer is right!

left to right: same order

Let's look back.

First: write each as a decimal.

Then: same number of digits.

Then: compare.

Then: write the answer.

Last: check.

Answer