Question

The result of $\left( {{\text{54}}{\text{.327 $\times$ 357}}{\text{.2 $\times$ 0}}{\text{.0057}}} \right)$ is same as
A. ${\text{5}}{\text{.4327 $\times$ 3}}{\text{.572 $\times$ 5}}{\text{.7}}$
B. ${\text{5}}{\text{.4327 $\times$ 3}}{\text{.572 $\times$ 0}}{\text{.57}}$
C. ${\text{54327 $\times$ 3572 $\times$ 0}}{\text{.0000057}}$
D. ${\text{5432}}{\text{.7 $\times$ 3}}{\text{.572 $\times$ 0}}{\text{.000057}}$

Answer 1

Hint: The expressions given to us are product of decimals. The number of decimal places before and after multiplication will be equal. So, the option with an equal number of decimal places as in the question will be the correct answer.

Complete step by step answer:

Decimal numbers are the numbers having their whole number part and fractional parts separated by a decimal point. The digits which come after the decimal points are called decimal places. The number of decimal places a decimal has is the number of digits present in the number after the decimal point.
We have the expression $\left( {{\text{54}}{\text{.327 $\times$ 357}}{\text{.2 $\times$ 0}}{\text{.0057}}} \right)$. This has a total of 8 decimal places.
As it is multiplication, the total number of decimal places will be the same after the multiplication. So, we can check through the options.
The 1st option is ${\text{5}}{\text{.4327 $\times$ 3}}{\text{.572 $\times$ 5}}{\text{.7}}$. It has a total decimal place of ${\text{4 + 3 + 1 = 8}}$.
The second option is ${\text{5}}{\text{.4327 $\times$ 3}}{\text{.572 $\times$ 0}}{\text{.57}}$. The total number of decimal places of this expression is ${\text{4 + 3 + 2 = 9}}$
The 3rd option is ${\text{54327 $\times$ 3572 $\times$ 0}}{\text{.0000057}}$. It has a total number of decimal places of 7
The last option is ${\text{5432}}{\text{.7 $\times$ 3}}{\text{.572 $\times$ 0}}{\text{.000057}}$ and have a total number of decimal places equal to${\text{1 + 3 + 6 = 10}}$
So, the only option matching with the number of decimal places in the question is option A.
Therefore, the correct answer is option A.

Note: Decimal numbers are numbers having their whole number part and fractional parts separated by a decimal point. The digits which come after the decimal points are called decimal places. The 1st place to the right of the decimal point is called the tenths place, 2nd place is called the hundredth place, and so on. Decimals in which a digit or set of digits repeats indefinitely are known as recurring decimals. Decimals that don’t end and don’t repeat are known as non-terminating and non-recurring decimals. These types of decimals cannot be written as fractions. The concept of simple decimal multiplication is used here. This property of decimal multiplication can be observed in the squaring of the decimal. We don’t need to do the actual multiplication for solving this problem, we can just solve it by observing the options.