Question

# If a decimal number is divided by 1000, then the decimal point shifts to the _____ by ______ positions.\begin{align} & \left( A \right)left,2 \\ & \left( B \right)right,3 \\ & \left( C \right)left,3 \\ & \left( D \right)right,2 \\ \end{align}

Hint: We solve this question by moving the decimals one by one according to the number of times we are dividing the decimal with 10. Then we can compare the number obtained after dividing with 1000 with the original number and find the number of positions that the decimal had shifted and the direction in which it has shifted.

As we were not given any decimal number, let us consider a decimal number say 1234.5
For the decimal number 1234.5, the whole number part is 1234 and the fractional part is 0.5.
So, let us place the fractional part on the right side of the decimal and whole number in the left side of the decimal.
The place value table of any decimal can be shown as
 Thousands Hundreds Tens Ones . Tenths Hundredths Thousandths 1000 100 10 1 $\dfrac{1}{10}$ $\dfrac{1}{100}$ $\dfrac{1}{1000}$ 1 2 3 4 5

When 1234.5 is divided by 10 we get 123.45. Dividing it again with 10 we get 12.345. Dividing it again with 10 we get 1.2345. So, when divided by 1000, we get 1.2345.
So, writing the place value table for 1.2345, we get
 Ones . Tenths Hundredths Thousandths Ten thousandths 1 $\dfrac{1}{10}$ $\dfrac{1}{100}$ $\dfrac{1}{1000}$ $\dfrac{1}{10000}$ 1 . 2 3 4 5

So, by comparing the above two tables we can see that digits are shifted 3 positions to the right and the decimal point has shifted to the left side by 3 positions.

So, the correct answer is “Option C”.

Note: There is a chance of making a mistake while solving this question by shifting the digits to left instead of shifting the digits to right. Suppose for the above taken example one might write the place value table as
 Thousands Lakhs Ten Thousands Thousands Hundreds Tens Ones 1000000 100000 10000 1000 100 10 1 1 2 3 4 5 0 0

But it is wrong because it occurs when the decimal is multiplied with 1000 not when divided with 1000.