While converting a fraction with denominator as a power of 10, we shift the decimal point to the left by a number of times equal to the ______ in the denominator.
(A) digits
(B) ones
(C) zeros
(D) power of 10
Answer
636.3k+ views
Hint: We use the concept of fraction which has a numerator and a denominator. Use the concept of conversion of fraction to a decimal number to find the correct option to be filled in the blank of the statement in the question.
* A fraction is the numerical quantity which is not a whole number. Example:\[\dfrac{1}{2} = 0.5\],\[\dfrac{1}{4} = 0.25\]etc.
* A decimal number is a number where we put a decimal point and there are some digits after that point. The digits in a number after the decimal point show the values that are less than 1.
Complete step-by-step solution:
We know a fraction\[\dfrac{a}{b}\]indicates that ‘a’ is divided by ‘b’.
So, if ‘a’ is not a factor of ‘b’ then the answer comes out to be a decimal number.
We have to convert a fraction having denominator as power of 10
Let the fraction be \[\dfrac{{1234}}{{{{10}^n}}}\]where \[n \geqslant 1\]
Now we check for few values of n
Put \[n = 1\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^1}}} = \dfrac{{1234}}{{10}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there is only one digit after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^1}}} = 123.4\]
Now
Put \[n = 2\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^2}}} = \dfrac{{1234}}{{100}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there are two digits after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^2}}} = 12.34\]
Now
Put \[n = 3\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^3}}} = \dfrac{{1234}}{{1000}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there are three digits after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^3}}} = 1.234\]
Similarly we continue for all other values of n
So, the value of n in the denominator gives us the value of digits that come after the decimal in the number.
So, we shift the decimal point to the left by a number of times equal to the power of 10 in the denominator.
\[\therefore \]The option (D) is correct.
Note: Students many times get confused while placing the decimal as they start counting the position from decimal point from left side. Keep in mind we always count the positions from the right hand side of the number.
* A fraction is the numerical quantity which is not a whole number. Example:\[\dfrac{1}{2} = 0.5\],\[\dfrac{1}{4} = 0.25\]etc.
* A decimal number is a number where we put a decimal point and there are some digits after that point. The digits in a number after the decimal point show the values that are less than 1.
Complete step-by-step solution:
We know a fraction\[\dfrac{a}{b}\]indicates that ‘a’ is divided by ‘b’.
So, if ‘a’ is not a factor of ‘b’ then the answer comes out to be a decimal number.
We have to convert a fraction having denominator as power of 10
Let the fraction be \[\dfrac{{1234}}{{{{10}^n}}}\]where \[n \geqslant 1\]
Now we check for few values of n
Put \[n = 1\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^1}}} = \dfrac{{1234}}{{10}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there is only one digit after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^1}}} = 123.4\]
Now
Put \[n = 2\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^2}}} = \dfrac{{1234}}{{100}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there are two digits after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^2}}} = 12.34\]
Now
Put \[n = 3\]
\[ \Rightarrow \dfrac{{1234}}{{{{10}^3}}} = \dfrac{{1234}}{{1000}}\]
We write the RHS of the equation as a decimal number where we place decimal such that there are three digits after the decimal.
\[ \Rightarrow \dfrac{{1234}}{{{{10}^3}}} = 1.234\]
Similarly we continue for all other values of n
So, the value of n in the denominator gives us the value of digits that come after the decimal in the number.
So, we shift the decimal point to the left by a number of times equal to the power of 10 in the denominator.
\[\therefore \]The option (D) is correct.
Note: Students many times get confused while placing the decimal as they start counting the position from decimal point from left side. Keep in mind we always count the positions from the right hand side of the number.
Recently Updated Pages
Find the greatest six digit number that is exactly class 8 maths CBSE

What is the time difference between India and Cana class 8 social science CBSE

Compare LPG and wood as fuels class 8 chemistry CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

30 opposite words in English from a to z class 8 english CBSE

How many cubic feet equals to 1 unit sand class 8 maths CBSE

Trending doubts
What is BLO What is the full form of BLO class 8 social science CBSE

Citizens of India can vote at the age of A 18 years class 8 social science CBSE

Full form of STD, ISD and PCO

One cusec is equal to how many liters class 8 maths CBSE

Who commanded the Hector the first British trading class 8 social science CBSE

What are the methods of reducing friction. Explain


