Which is bigger, 0.444... or 0.45

Step by step

The question

Question: which is bigger, 0.444… or 0.45?

1 Same number of digits

Zeros at the end of a decimal do not change it: 0.45 is the same as 0.450.

A repeating decimal goes on for ever, so we can write as many of its digits as we need.

So we give every number 3 digits after the point.

2 Compare

Now both have 3 digits after the point.

So we can forget the point and compare them like whole numbers: 444 < 450.

3 Write the answer

Now with the numbers as they were given: 0.444… < 0.45.

So 0.45 is bigger.

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: 0.444…, 0.45.

The same order.

So the answer is right!

Let's look back.

First: same number of digits.

Then: compare.

Then: write the answer.

Last: check.