We can observe that
2.4 = 24/10
2.47 = 247/102
2.479 = 2479/103
From the above examples, it is clear that depending on the position of the decimal point, a decimal number can be converted to a fraction such with denominator as a power of 10. That is 10 , 102 or 103.
What if a decimal number is multiplied by 10 , 102 or 103?
Consider the following examples
2.79 x 10 = 27.9
In the above multiplication, since we multiply 2.79 by 10 to the first power, decimal point is moved 1 digit to the right.
2.798 x 102 = 279.8
In the above multiplication, since we multiply 2.798 by 10 to the second power, decimal point is moved two digits to the right.
Similarly. if you multiply a number by 10 to the third power, decimal point has to be moved three digits to the right, by 10 to the fourth power, decimal point has to be moved four digits to the right and so on.
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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