## What you need to know

Things to remember:

• If we have a 1 and lots of 0s, like 10 000, the number of 0s is how many times we multiply by 10. Multiply by 10 000 means we multiply by 10 five times.
• Each time we multiply by 10 the numbers move left one place.
• If we have lots of 0s on the end of a decimal number, we can remove them 23.5600=23.56

Our first few powers of 10 are:

10                    100                  1 000               10 000             100 000

So, how do we multiply by these numbers? Let’s start by looking at 23.56

$$Hundredths\rightarrow 6$$

$$Tenths\rightarrow 5$$

$$Units\rightarrow 3$$

$$Tens\rightarrow 2$$

But, what would happen if we added some 0s to 23.56?

0023.5600

We have added 0 thousands, 0 hundreds, 0 thousandths, and 0 ten thousandths. So, really, we haven’t added anything!

23.56 = 0023.5600

Before looking at 23.56 in more detail, let’s look at an easier number we know how to multiply by 10.

$$5\times10=50$$

What happens if we add some 0s to the 5?

$$005.00\times10=050.00$$

So, as we can see, when we multiply by 10, we just move all of the numbers left one place! So, how do we do this with the 23.56?

$$23.56\times10=235.6$$

We just moved everything left one place!

So, how do we multiply by bigger powers, like 100, 1 000, 10 000, etc? We need to remember, that we get these by multiply by 10.

$$10= 1 \times10$$

$$100= 10 \times10$$

$$1000= 10 \times10\times10$$

$$10000 = 10\times10 \times10\times10$$

We get these numbers by multiply by 10 lots of times. So, we need to learn two important points:

• Each time we multiply by 10 the numbers move left.
• The number of 0s in a power of 10 means how many times we multiply by 10.

So, putting these two points together, we can make a third SUPER important point:

• Each 0 means we move the numbers left 1.

10 means we move left once.

100 means we move left twice.

1000 means we move left three times

10000 means we move left four times

Etc.

So, let’s get back to our 23.56.

$$23.56 \times100=2356$$

What about if we multiply by something bigger, like 1,000? Once we run out of decimal numbers, we just start adding 0s!

$$23.56 \times1000=23560$$

$$23.56 \times10000=235600$$

## Example Questions

We are multiplying by 100, which means the numbers move left twice.

$$23.56 \times1,000=56786$$

We are multiplying by 10,000, which means the numbers move left 4 times. Remember, once we run out of decimal numbers, we start adding 0s to the end.

$$7.895 \times10,000=78,950$$