# MULTIPLYING DECIMALS by 10 100 and 1000

It is observed that

3.7  =  37/10

3.72  =  372/100

3.723  =  3723/1000

Thus, it is found that depending on the position of the decimal point, the decimal number can be converted to a fraction with denominator 10 , 100 or 1000.

Now let us see what would happen if a decimal number is multiplied by 10 or 100 or 1000.

For example,

3.23 x 10  =  (323/100) x 10  =  323/10  =  32.3

In the above multiplication, since 10 has one zero, decimal point shifted to the right by one place.

3.23 x 100  =  (323/100) x 100  =  323

In the above multiplication, since 100 has two zeros, decimal point shifted to the right by two places.

3.23 x 1000  =  (323/100) x 1000  =  323 x 10  =  3230

In the above multiplication, since 1000 has three zeros, decimal point shifted to the right by three places.

## Practice Problems

Problem 1 :

Multiply 3.723 by 10

Solution :

We multiply by 3.723 by 10. So, we have to move the decimal point one digit to the right.

Then,

3.723 x 10  =  37.23

Multiplying 3.723 by 10, we get 37.23

Problem 2 :

Multiply 3.723 by 100

Solution :

We multiply by 3.723 by 100. So, we have to move the decimal point two digits to the right.

Then,

3.723 x 100  =  372.3

Multiplying 3.723 by 100, we get 372.3

Problem 3 :

Multiply 3.723 by 1000

Solution :

We multiply by 3.723 by 1000. So, we have to move the decimal point two digits to the right.

Then,

3.723 x 1000  =  3723

Multiplying 3.723 by 1000, we get 3723

Problem 4 :

The price of a fruit is \$3.52 per lb. Find the cost of 10 lbs of fruits.

Solution :

Given : Cost of 1 lb of fruit  =  \$3.52

Then, the cost of 10 lbs of fruits is

=  10 x 3.52

We multiply by 3.52 by 10. So, we have to move the decimal point one digit to the right.

So, we get

=  35.2

So, the cost of 10 lbs of fruits is \$35.2

Problem 5 :

A person walks regularly in the morning. If the speed of his walking is 43.26 ft per minute, Find the distance covered by him in  100 minutes.

Solution :

Given : Speed is 43.26 ft per minute.

So, distance covered in one minute is 43.26 ft.

We all know the formula for distance.

That is,

Distance  =  Speed x Time

To know the distance covered in 100 minutes, we have to plug time  =  100 and the speed is 43.26

Distance  =  43.26 x 100

We multiply by 43.26 by 100. So, we have to move the decimal point two digits to the right.

So, we get

Distance  =  4326 ft

So, the distance covered by him in  100 minutes is 4326 ft.

Problem 6 :

One-thousandth of a certain number is 0.003. What is the number?

Solution :

Given : One-thousandth of a certain number is 0.003

Let "a" be the number.

Then, from the given information, we get

(1/1000) x a  =  0.003

Multiplying by 1000 on both sides, we get

a  =  0.003 x 1000

We multiply by 0.003 by 1000. So, we have to move the decimal point three digits to the right.

So, we get

a  =  3

So, the the number is 3. Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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