MULTIPLYING DECIMALS BY POWERS OF 10 WORKSHEET

Problem 1 :

Evaluate :

7.285 x 10

Solution :

Since 7.285 is multiplied by 10, the decimal point has to shifted one digit to the right.

Therefore,

7.285 x 10 = 72.85

Problem 2 :

Evaluate :

7.285 x 100

Solution :

Since 7.285 is multiplied by 100, the decimal point has to shifted two digits to the right.

Therefore,

7.285 x 100 = 728.5

Problem 3 :

Evaluate :

7.285 x 1000

Solution :

Since 7.285 is multiplied by 1000, the decimal point has to shifted three digits to the right.

Therefore,

7.285 x 1000 = 7285

Problem 4 :

Evaluate :

0.064 x 10²

Solution :

Since 0.064 is multiplied by 10², the decimal point has to be shifted two digits to the right.

Therefore,

0.064 x 10² = 6.4

Problem 5 :

Evaluate :

0.00265 x 10³

Solution :

Since 0.00265 is multiplied by 10³, the decimal point has to be shifted three digits to the right.

Therefore,

0.00265 x 10³ = 2.65

Problem 6 :

Multiply :

0.03007 x 10⁴

Solution :

Since 0.003007 is multiplied by 10⁴, the decimal point has to be shifted four digits to the right.

Therefore,

0.03007 x 10⁴ = 300.7

Problem 7 :

The cost of an apple is $1.36. What is the cost of 100 apples? 

Solution :

It is given that the cost of 1 apple is $1.36.

The cost of 100 apples :

= 100 x 1.36

Since 1.36 is multiplied by 100, the decimal point has to be shifted two digits to the right.

= $136

Problem 8 :

Pencils come in packages of 14 and each package costs $10.50. Find the cost of 10 pencils.

Solution :

It is given that the cost of 1 package of pencils is $10.50.

14 pencils ----> $10.50

1 pencil ----> (10.50/14) = $0.75

The cost of 10 pencils :

= 10 x 0.75

Since 0.75 is multiplied by 10, the decimal point has to be shifted one digit to the right.

= $7.50

Problem 9 :

A car runs at a rate of 57.568 miles per hour. Find the distance covered by the car in 10 hours.

Solution :

It is given that the car runs at a rate of 57.568 miles per hour.

That is, the distance covered by the car in one hour is 57.568 miles.

To find the distance covered by the car in 10 hours, 57.568 has to be multiplied by 10. 

= 57.568 x 10

Since 57.568 is multiplied by 10, the decimal point has to be shifted one digit to the right.

= 575.68

Therefore, the distance covered by the car in 10 hours is 575.68 miles.

Problem 10 :

Lily walks regular in the morning at a rate of 1.276 ft. per second. At the same rate, find the distance covered by her in 100 minutes. 

Solution :

It is given that Like walks 1.5 ft. in one second.

1 second ----> 1.276 ft.

60(1 second) ----> 60(1.276 ft.)

60 seconds ----> 76.56 ft.

1 minute ----> 76.56 ft.

Distance covered by Lily in 100 minutes :

= 100 x 76.56

Since 76.56 is multiplied by 100, the decimal point has to be shifted two digits to the right.

= 7656 ft.

Problem 11 :

Mr. Jones travels at an average speed of  drives his car at a rate of 72.84 miles per hour. Find the distance covered by him in 10 minutes.

Solution :

It is given that the speed is 72.84 miles per hour.

That is, distance covered in one hour is 72.84 miles.

1 hour ----> 72.84 miles

60 minutes ----> 72.84 miles

1 minute ----> (72.84/60) miles

1 minute ----> 1.214 miles

Distance covered in one minute is 1.214 miles.

Distance covered by Mr. Jones in 10 minutes :

= 1.214 x 10

Since 1.214 is multiplied by 10, the decimal point has to be shifted one digit to the right.

= 12.14 miles

Problem 12 :

If one-hundredth of a number is 0.04, find the number.

Solution :

It is given that one-hundredth of a number is 0.04.

Let a be the number.

From the given information,

(1/100) x a = 0.04

Multiply both sides by 100.

a = 0.04 x 100

Since 0.04 is multiplied by 100, the decimal point has to be shifted two digits to the right.

a = 4 

The number is 4.

Problem 13 :

When 7.K89 is multiplied by 10², the answer is 758.9. Find the value of K.

Solution :

Since 7.K89 is multiplied by 10², the decimal point has to be shifted two digits to the right.

7.K89 x 10² = 7K8.9

It is given that the product 7.K89 and 10 is 758.9.

7K8.9 = 758.9

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

K = 5

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