Question

Which of the following values is equal to 1?
A. $\dfrac{{0.304 \times 20}}{{304 \times 2}}$
B. $\dfrac{{0.304 \times 20}}{{3.04 \times 2}}$
C. $\dfrac{{0.304 \times 2}}{{30.4 \times 2}}$
D. $\dfrac{{0.304 \times 2}}{{304 \times 0.2}}$

Answer 1

Hint: This problem deals with basic and a very simple concept in mathematics, which is multiplication of decimals. In order to solve this problem we should be able to multiply the decimal numbers with each other, and should be able to divide the obtained decimal numbers with the other decimals obtained which are given in the options above.

Complete step-by-step solution:
Given a few numbers of options above and from those options we have to find out the right option which gives the equal to the number 1.
So checking through each option, whether any of the options gives an equal to 1.
Starting from the first option as given below:
Consider the first option which is, $\dfrac{{0.304 \times 20}}{{304 \times 2}}$ , and simplify to check whether it gives an equal to 1, as given below:
$ \Rightarrow \dfrac{{0.304 \times 20}}{{304 \times 2}} = \dfrac{{6.08}}{{608}}$
$ \Rightarrow \dfrac{{6.08}}{{608}} = 0.01$
$\therefore \dfrac{{0.304 \times 20}}{{304 \times 2}} = 0.01$
Hence $\dfrac{{0.304 \times 20}}{{304 \times 2}} \ne 1$
Thus the first option is not equal to 1.
Now consider the second option which is, $\dfrac{{0.304 \times 20}}{{3.04 \times 2}}$ , and simplify to check whether it gives an equal to 1, as given below:
$ \Rightarrow \dfrac{{0.304 \times 20}}{{3.04 \times 2}} = \dfrac{{6.08}}{{6.08}}$
$ \Rightarrow \dfrac{{6.08}}{{6.08}} = 1$
$\therefore \dfrac{{0.304 \times 20}}{{3.04 \times 2}} = 1$
Hence $\dfrac{{0.304 \times 20}}{{3.04 \times 2}} = 1$
Thus the second option is equal to 1.
Now consider the third option which is, $\dfrac{{0.304 \times 2}}{{30.4 \times 2}}$, and simplify to check whether it gives an equal to 1, as given below:
$ \Rightarrow \dfrac{{0.304 \times 2}}{{30.4 \times 2}} = \dfrac{{0.608}}{{60.8}}$
$ \Rightarrow \dfrac{{0.608}}{{60.8}} = 0.01$
$\therefore \dfrac{{0.304 \times 2}}{{30.4 \times 2}} = 0.01$
Hence $\dfrac{{0.304 \times 2}}{{30.4 \times 2}} \ne 1$
Thus the third option is also not equal to 1.
Now consider the fourth option which is, $\dfrac{{0.304 \times 2}}{{304 \times 0.2}}$, and simplify to check whether it gives an equal to 1, as given below:
$ \Rightarrow \dfrac{{0.304 \times 2}}{{304 \times 0.2}} = \dfrac{{0.608}}{{60.8}}$
$ \Rightarrow \dfrac{{0.608}}{{60.8}} = 0.01$
$\therefore \dfrac{{0.304 \times 2}}{{304 \times 0.2}} = 0.01$
Hence $\dfrac{{0.304 \times 2}}{{304 \times 0.2}} \ne 1$
Thus the fourth option is also not equal to 1.
Hence all the options except one option are equal to 0.01.
Only option B is equal to 1.
Here option B is $\dfrac{{0.304 \times 20}}{{3.04 \times 2}} = 1$.

Hence option B is the correct answer.

Note: Here while solving the problem, first we should understand what decimal numbers are. Decimals are also called the Hindu-Arabic numbers, or Arabic system, or number system. In mathematics, the positional numeral system employs 10 as the base and requires 10 different numerals, the digits, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. It also requires a dot (decimal point) to represent decimal fractions.