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.
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.
Problem 1 :
Multiply 3.723 by 10
We multiply by 3.723 by 10. So, we have to move the decimal point one digit to the right.
3.723 x 10 = 37.23
Multiplying 3.723 by 10, we get 37.23
Problem 2 :
Multiply 3.723 by 100
We multiply by 3.723 by 100. So, we have to move the decimal point two digits to the right.
3.723 x 100 = 372.3
Multiplying 3.723 by 100, we get 372.3
Problem 3 :
Multiply 3.723 by 1000
We multiply by 3.723 by 1000. So, we have to move the decimal point two digits to the right.
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.
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
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.
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.
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?
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.
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