Order 0.4, 3/8, -1/2, 3/5 from smallest to largest Step by Step

Step by step

The question

Question: put 0.4, 3/8, −1/2, 3/5 in order, from smallest to largest.

0.4, 38, −12, 35

1 Write each as a decimal

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

A decimal is tenths, hundredths or thousandths.

8 times 125 is 1000.

So we multiply the top and the bottom by 125.

375 thousandths is 0.375.

So 3/8 is 0.375.

= 38 = 3 × 1258 × 125 = 3751000 = 0.375

2 times 5 is 10.

So we multiply the top and the bottom by 5.

5 tenths is 0.5.

The minus sign stays in front: −0.5.

= −12 = −1 × 52 × 5 = −510 = −0.5

5 times 2 is 10.

So we multiply the top and the bottom by 2.

6 tenths is 0.6.

So 3/5 is 0.6.

= 35 = 3 × 25 × 2 = 610 = 0.6

2 Same number of digits

Zeros at the end of a decimal do not change it: 0.4 is the same as 0.400.

So we give every number 3 digits after the point.

= 0.400, 0.375, −0.500, 0.600

3 Compare

Now they all have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 375 < 400 < 600.

= 0.375 < 0.400 < 0.600

375 < 400 < 600

Careful!

More digits does not mean bigger.

Compare 0.375 with 0.400.

Careful: not 0.375 > 0.4 ✗

Negative numbers are smaller than every positive number.

So they come first.

= −0.500 < 0.375 < 0.400 < 0.600

4 Write the answer

Now we write the numbers as they were given, in the same order: −1/2, 3/8, 0.4, 3/5.

= −12 < 38 < 0.4 < 35

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: −1/2, 3/8, 0.4, 3/5.

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