## What you need to know

Things to remember:

• To compare numbers we start from the biggest place value and work towards the right until we find two numbers that are different.

Comparing numbers, we need to look at the place values of each digit in a number. Let’s look at 235,487.

$$Hundred\hspace{1em}Thousands\rightarrow 2$$

$$Ten\hspace{1em}Thousands\rightarrow 3$$

$$Thousands\rightarrow 5$$

$$Hundreds\rightarrow 4$$

$$Tens\rightarrow 8$$

$$Units\rightarrow 7$$

So, how do we compare two numbers? How would we decide which is smaller out of 5674 and 5655? We start by comparing the value of the thousands and work from left to right until we find numbers that are different.

$$Thousands\rightarrow 5$$

$$Thousands\rightarrow 5$$

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. But we don’t always look for the smallest.

We can do the exact same thing for larger numbers, just remember to start from the left and go towards the right.

Which number is bigger, 235,655 or 235,778? Start by looking at the biggest place value, which is the hundreds of thousands.

$$Hundred\hspace{1em}Thousands\rightarrow 2$$

$$Hundred\hspace{1em}Thousands\rightarrow 2$$

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

$$Ten\hspace{1em}Thousands\rightarrow 3$$

$$Ten\hspace{1em}Thousands\rightarrow 3$$

Both numbers have the same amount of tens of thousands, so we need to move onto the thousands.

$$Thousands\rightarrow 5$$

$$Thousands\rightarrow 5$$

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

$$Hundreds\rightarrow 6$$

$$Hundreds\rightarrow 7$$

We have a difference! We are looking for the biggest number, and we know that 7 is bigger than 6, so 235,778 must be bigger than 235,655.

## Example Questions

#### Question 1: Which is bigger, 561,788 or 565,221?

Start by comparing the hundreds of thousands.

$$Hundred\hspace{1em}Thousands\rightarrow 5$$

$$Hundred\hspace{1em}Thousands\rightarrow 5$$

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

$$Ten\hspace{1em}Thousands\rightarrow 6$$

$$Ten\hspace{1em}Thousands\rightarrow 6$$

Both numbers have the same amount of tens of thousands, so we need to move onto the thousands.

$$Thousands\rightarrow 1$$

$$Thousands\rightarrow 5$$

We have a difference! We are looking for the biggest number, and we know that 5 is bigger than 1, so 565,221 must be bigger than 561,788.

#### Question 2: Which is smaller, 674,554 or 644,554?

Start by comparing the hundreds of thousands.

$$Hundred\hspace{1em}Thousands\rightarrow 6$$

$$Hundred\hspace{1em}Thousands\rightarrow 6$$

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

$$Ten\hspace{1em}Thousands\rightarrow 7$$

$$Ten\hspace{1em}Thousands\rightarrow 4$$

We have a difference! We are looking for the smallest number, and we know that 4 is smaller than 7, so 644,554 is smaller than 674,554.