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Order 0.6, 0.06, 0.66 from smallest to largest

Step by step, with the reason for every step · Comparing and ordering numbers · Foundations

Step by step

The question

Question: put 0.6, 0.06, 0.66 in order, from smallest to largest.

0.6, 0.06, 0.66

1 Same number of digits

Zeros at the end of a decimal do not change it: 0.6 is the same as 0.60.

So we give every number 2 digits after the point.

= 0.60, 0.06, 0.66

2 Compare

Now they all have 2 digits after the point.

So we can forget the point and compare them like whole numbers: 6 < 60 < 66.

= 0.06 < 0.60 < 0.66
6 < 60 < 66

Careful!

More digits does not mean bigger.

Compare 0.06 with 0.60.

Careful: not 0.06 > 0.6 ✗

3 Write the answer

Now we write the numbers as they were given, in the same order: 0.06, 0.6, 0.66.

= 0.06 < 0.6 < 0.66

4 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: 0.06, 0.6, 0.66.

The same order.

So the answer is right!

left to right: same order

Let's look back.

First: same number of digits.

Then: compare.

Then: write the answer.

Last: check.

Answer
= 0.06 < 0.6 < 0.66

Your turn

Try this one yourself, then check:

Put 0.4, 0.31, 0.82
Show the answer
0.31 < 0.4 < 0.82

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