MULTIPLYING DECIMALS BY POWERS OF 10

Problem 1 :

Multiply :

5.679 x 10

Solution :

Since we multiply by 5.679 by 10, we have to shift the decimal point to the right by one place.

Therefore,

5.679 x 10 = 56.79

Problem 2 :

Multiply :

5.679 x 100

Solution :

Since we multiply by 5.679 by 100, we have to shift the decimal point to the right by two places.

Therefore,

5.679 x 100 = 567.9

Problem 3 :

Multiply :

5.679 x 1000

Solution :

Since we multiply by 5.679 by 1000, we have to shift the decimal point to the right by three places.

Therefore,

5.679 x 1000 = 5679

Problem 4 :

Multiply :

0.75 x 10²

Solution :

Since we multiply by 0.75 by 10², we have to shift the decimal point to the right by two places.

Therefore,

0.75 x 10² = 75

Problem 5 :

Multiply :

0.0038 x 10³

Solution :

Since we multiply by 0.0038 by 10³, we have to shift the decimal point to the right by three places.

Therefore,

0.0038 x 10³ = 3.8

Problem 6 :

Multiply :

0.01005 x 10⁴

Solution :

Since we multiply by 0.01005 by 10⁴, we have to shift the decimal point to the right by four places.

Therefore,

0.01005 x 10⁴ = 100.5

Problem 7 :

If the price of a pencil is $0.75, find the total cost of 10 pencils. 

Solution :

Given : Cost of 1 pencil = $0.75.

Then, the cost of 10 pencils is

= 10 x 0.75

Since we multiply by 0.75 by 10, we have to shift the decimal point to the right by one place.

= 7.5

So, the cost of 10 pencils is $7.50.

Problem 8 :

The cost of one box of erasers is $37.50. If a box contains contains 30 erasers, find the cost of 100 erasers. 

Solution :

Given : Cost of 1 box of erasers = $37.50.

30 erasers ----> $37.50

1 eraser ----> (37.50/30) = $1.25

The cost of 100 erasers :

= 100 x 1.25

Since we multiply by 1.25 by 100, we have to shift the decimal point to the right by two places.

= $125

Problem 9 :

Mr. Daniel walks regularly in the morning and the speed of his walking is 42.25 ft. per minute. Find the distance covered by him in  100 minutes. 

Solution :

Given : Speed of walking is 43.26 ft. per minute.

Formula to find distance :

Distance = Speed x Time

Substitute speed = 42.25 and time = 100.

= 42.25 x 100

Since we multiply by 42.25 by 100, we have to shift the decimal point to the right by two places.

Distance = 42.25 ft.

The distance covered by Mr. Daniel in 100 minutes is 4225 ft.

Problem 10 :

Mr. Adam drives his car at a rate of 48.84 miles per hour. Find the distance covered by him in 100 minutes.

Solution :

Given : Speed is 48.84 miles per hour.

That is, distance covered in one hour is 48.84 miles.

1 hour ----> 48.84 miles

60 minutes ----> 48.84 miles

1 minute ----> (48.84/60) miles

1 minute ----> 0.814 miles

Distance covered in one minute is 0.814 miles.

Distance covered by Mr. Adam in 100 minutes :

= 0.814 x 100

Since we multiply by 0.814 by 100, we have to shift the decimal point to the right by two places.

= 81.4 miles

Problem 11 :

One-hundredth of a certain number is 0.07. What is the number?

Solution :

Given : One-hundredth of a certain number is 0.07.

Let k be the number.

From the given information,

(1/100) x k = 0.07

Multiply both sides by 100.

k = 0.07 x 100

Since we multiply by 0.07 by 100, we have to shift the decimal point to the right by two places.

k = 7 

So, the number is 7.

Problem 12 :

The product of 1.y74 and 10² is 137.4. What is the value of k?

Solution :

Since we multiply 1.y74 by 10², we have to shift the decimal point to the right by two places.

1.y74 x 10² = 1y7.4

Given : The product 0.07k6 and 10² is 1y7.4.

1y7.4 = 137.4

Since the two numbers above are equal, the digits at tens place on the left side and the digit side must be equal.

y = 3

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