Question

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 1

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.