Problems 1-10 : Evaluate each of the following divisions.
Problem 1 :
27.9 ÷ 10
Problem 2 :
209.3 ÷ 100
Problem 3 :
54002.7 ÷ 1000
Problem 4 :
18312.4 ÷ 10000
Problem 5 :
16 ÷ 10
Problem 6 :
7 ÷ 10
Problem 7 :
99 ÷ 100
Problem 8 :
1.7 ÷ 100
Problem 9 :
0.65 ÷ 10
Problem 10 :
0.09 ÷ 1000
Problem 11 :
If 10 pencils cost $7.50, find the cost of one pencil.
Problem 12 :
If a man walks 3562.7 ft. of distance in 100 minutes, how many feet of distance will he walk in one minute?
Problem 13 :
A flight travels a distance of 7905.6 miles in 16 hours 40 minutes. Find the distance covered by the flight in one minute.
Problem 14 :
If the decimal number 943.Y7 is divided by 100, the answer is 9.4357. Find the value of Y.
1. Answer :
Since we divide 27.9 by 10, we have to move the decimal point to the left by one digit.
Therefore,
27.9 ÷ 10 = 2.79
2. Answer :
Since we divide 209.3 by 100, we have to move the decimal point to the left by two digits.
Therefore,
209.3 ÷ 100 = 2.093
3. Answer :
Since we divide 54002.7 by 1000, we have to move the decimal point to the left by three digits.
Therefore,
54002.7 ÷ 1000 = 54.0027
4. Answer :
Since we divide 18312.4 by 10000, we have to move the decimal point to the left by four digits.
Therefore,
18312.4 ÷ 10000 = 1.83124
5. Answer :
Here 16 is divided by 10 and 16 is a whole number.
Since we divide 16 by 10, take decimal point in 16 such that there is one digit to the right of the decimal point.
Therefore,
16 ÷ 10 = 1.6
6. Answer :
Here 7 is divided by 10 and 7 is a whole number.
Since we divide 7 by 10, take decimal point in 7 such that there is one digit to the right of the decimal point.
Therefore,
7 ÷ 10 = 0.7
7. Answer :
Here 99 is divided by 100 and 99 is a whole number.
Since we divide 99 by 100, take decimal point in 99 such that there are two digits to the right of the decimal point.
Therefore,
99 ÷ 100 = 0.99
8. Answer :
Since we divide 1.7 by 100, we have to move the decimal point to the left by two digits. But, we have only one digit to the left of the decimal point. To get one more digit, we have to add one zero.
1.7 ÷ 100 = 0.017
9. Answer :
Since we divide 0.65 by 10, we have to move the decimal point to the left by one digit. But, we have no digit to the left of the decimal point. To get one digit, we have to add one zero.
0.65 ÷ 10 = 0.065
10. Answer :
Since we divide 0.09 by 1000, we have to move the decimal point to the left by three digits. But, we have no digit to the left of the decimal point. To get three digits, we have to add three zeros.
0.09 ÷ 1000 = 0.00009
11. Answer :
To get the cost of one pencil. divide the total cost of 10 pencils by 10.
= 7.50/10
= 7.5 ÷ 10
= ⁷⁵⁄₁₀ ÷ ¹⁰⁄₁
Change the division to multiplication by taking reciprocal of ¹⁰⁄₁.
= ⁷⁵⁄₁₀ x ⅒
= ⁷⁵⁄₁₀₀
75 is a whole number. Since we divide 75 by 100, we have to take decimal point in 75such that there are two digits to the right of the decimal point.
= 0.75
The cost of one pencil is $0.75.
12. Answer :
To find the distance covered in one minute, we have to divide the distance covered in 100 minutes by 100.
= 3562.7/100
= 3562.7 ÷ 100
= ³⁵⁶²⁷⁄₁₀ ÷ ¹⁰⁰⁄₁
Change the division to multiplication by taking reciprocal of ¹⁰⁰⁄₁.
= ³⁵⁶²⁷⁄₁₀ x ¹⁄₁₀₀
= ³⁵⁶²⁷⁄₁₀₀₀
35267 is a whole number. Since 35627 is divided by 1000, take decimal point in 35627 such that there are three digits to the right of the decimal point.
= 35.627
The man will walk 35.627 ft. of distance in one minute.
13. Answer :
16 hours 40 minutes = (16 x 60) minutes + 40 minutes
= 960 minutes + 40 minutes
= 1000 minutes
Given : 7905.6 miles of distance covered in 16 hours 40 minutes.
16 hours 40 minutes ----> 7905.6 miles
1000 minutes ----> 7905.6 miles
1 minute ----> (7905.6/1000) miles
= 7905.6/1000
= 7905.6 ÷ 1000
= ⁷⁹⁰⁵⁶⁄₁₀ ÷ ¹⁰⁰⁰⁄₁
Change the division to multiplication by taking reciprocal of ¹⁰⁰⁰⁄₁.
= ⁷⁹⁰⁵⁶⁄₁₀ x ¹⁄₁₀₀₀
= ⁷⁹⁰⁵⁶⁄₁₀₀₀₀
79056 is a whole number. Since we divide 79056 by 10000, we have to take decimal point in 79056 such that there are four digits to the right of the decimal point.
= 7.9056
The distance covered by the flight in one minute is 7.9056 ft.
14. Answer :
When we divide the decimal number 943.Y7 by 100, we have to move the decimal point to the left by two digits.
943.Y7 ÷ 100 = 9.43Y7 ----(1)
Given : When 943.Y7 is divided by 100, the answer is 9.4357.
943.Y7 ÷ 100 = 9.4357 ----(1)
Comparing (1) and (2),
9.43Y7 = 9.4357
In the equality of two decimal numbers above, comparing the digits at thousandths places,
Y = 5
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