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

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