 ## What you need to know

Things to remember:

• We add as many zeros as there were at the ends of the two numbers.
• The final answer could have more zeros than there were at the start..

Let’s start by recapping what happens when we multiply numbers, by 10, 100, and 1000.

Number           Multiplying by 10         Multiplying by 100       Multiplying by 1000

15                         150                                    1500                                 15000

183                       1830                               18300                                183000

250                       2500                               25000                              250000

So, when we multiply a number by a power of 10, we add as many 0s as there in the power of 10. It is also important to notice how we can write numbers than end in lots of 0s.

$$183000=183\times1000$$

$$150=15\times10$$

What is the value of $37\times52000$

We can do this in four steps.

Step 1: Write the number with the zeros as a multiplication.

$$52000=52\times1000$$

Step 2: Replace the number with the 0s with the multiplication found in Step 1.

$$37\times52000=37\times52\times1000$$

Step 3: Multiply the numbers without the 0s.

$$37\times52=1924$$

Step 4: Multiply by the power of 10 (add the zeros)

$$37\times52000=1924000$$

Sometimes though, both numbers will have zeros.

What is the value of $9700\times35000$

We can do this in five steps.

Step 1: Write the numbers with the zeros as a multiplication.

$$9700=97\times100$$

$$35000=35\times1000$$

Step 2: Replace the numbers with the 0s with the multiplications found in Step 1.

$$9700\times35000=97\times100\times35\times1000$$

Step 3: Rearrange so the numbers without 0s are together

$$9700\times35000=97\times35\times1000 \times100$$

Step 4: Multiply the numbers without the 0s.

$$97\times35=3395$$

Step 4: Multiply by the powers of 10 (add the zeros)

$$9700\times35000=3395\times1000 \times100 =3395000000$$

## Example Questions

Step 1: Write the number with the zeros as a multiplication.

$$5800=58\times100$$

Step 2: Replace the number with the 0s with the multiplication found in Step 1.

$$13\times5800=13\times58\times100$$

Step 3: Multiply the numbers without the 0s.

$$13\times58=754$$

Step 4: Multiply by the power of 10 (add the zeros)

$$13\times5800=75400$$

Step 1: Write the numbers with the zeros as a multiplication.

$$270=27\times10$$

$$6100=61\times100$$

Step 2: Replace the numbers with the 0s with the multiplications found in Step 1.

$$270\times6100=27\times10\times61\times100$$

Step 3: Rearrange so the numbers without 0s are together

$$270\times6100=27\times61\times10 \times100$$

Step 4: Multiply the numbers without the 0s.

$$27\times61=1647$$

Step 4: Multiply by the powers of 10 (add the zeros)

$$270\times6100=1647\times10 \times100 =1647000$$