What you need to know

Things to remember:

  • Compare the digits in both numbers, going from left to right, until you find two digits that are different.
  • If you’re looking for a bigger number, choose the one with the bigger digit.
  • If you’re looking for a smaller number, choose the one with the smaller digit.

Let’ start by reminding ourselves how we compare two numbers.

Which is smaller, 5674 or 5655?

We start by comparing the left most place value, which is the thousands.

Thousands\rightarrow 5

Thousands\rightarrow 5

Both numbers have the same thousands, so we need to move onto the hundreds.

Hundreds\rightarrow 6

Hundreds\rightarrow 6

The hundreds are the same as well, so now we need to move onto the tens.

Tens\rightarrow 7

Tens\rightarrow 5

Now that we have numbers that are different, we can look for the smaller number. The smaller number is 5, so 5655 is smaller than 5674.

We do this in the exact same way with decimals!

Which is smaller, 2.456 or 2.456?

Start by comparing the units.

Units\rightarrow 2

Units\rightarrow 2

Both numbers have the same units, so we have to move right to the tenths.

Tenths\rightarrow 4

Tenths\rightarrow 4

The tenths here are the same, so we have to move right again, to the hundredths.

Hundredths\rightarrow 5

Hundredths\rightarrow 6

We have a difference! We are looking for the smaller number, and we know that 5 is smaller than 6, so 2.456 must be smaller than 2.466!

Example Questions

Question 1: Which is bigger, 5.446 or 5.476?

Answer

Start by comparing the units.

Units\rightarrow 5

Units\rightarrow 5

Both numbers have the same units, so we have to move right to the tenths.

Tenths\rightarrow 4

Tenths\rightarrow 4

The tenths here are the same, so we have to move right again, to the hundredths.

Hundredths\rightarrow 4

Hundredths\rightarrow 7

We have a difference! We are looking for the bigger number, and we know that 7 is bigger than 4, so 5.476 must be smaller than 5.446!

Question 2: Which is smaller 9.824 or 9.823?

Answer

Start by comparing the units.

Units\rightarrow 9

Units\rightarrow 9

Both numbers have the same units, so we have to move right to the tenths.

Tenths\rightarrow 8

Tenths\rightarrow 8

The tenths here are the same, so we have to move right again, to the hundredths.

Hundredths\rightarrow 2

Hundredths\rightarrow 2

The hundredths are the same as well, so we have to now look at the thousandths.

Thousandths\rightarrow 4

Thousandths\rightarrow 3

We have a difference! We are looking for the smaller number, and we know that 3 is smaller than 4, so 9.824 must be smaller than 9.823!