Question

Solve the following: $53.7 \times 10$.

Answer 1

Hint: First we need to express the decimal form into fractional form. To convert a decimal into a fraction we first write the number in the numerator and put $1$ in the denominator. Then we multiply both the numerator and denominator by $10$ for every digit after the decimal point. Multiplication of two fractions is given by multiplication of two numerators followed by multiplication of two denominators. The resultant fraction so formed is further reduced to its lowest terms by simplifying the terms of the fraction.

Complete step-by-step answer:
We need to find the product of the terms $53.7$ and $10$.
So we first convert the decimal $53.7$ into a fraction. So here we have one digit after the decimal point so we need to multiply both numerator and denominator by $10$.
The fractional form of $53.7$ is
$53.7 = \dfrac{{53.7}}{1}$
$ \Rightarrow 53.7 = \dfrac{{53.7 \times 10}}{{1 \times 10}}$
$ \Rightarrow 53.7 = \dfrac{{537}}{{10}}$
Therefore, the fractional form of $53.7$ is $\dfrac{{537}}{{10}}$.
Now we multiply the fractional form of $53.7$ with $10$.
So we first multiply both the numerators and denominators of the two numbers.
$\dfrac{{537}}{{10}} \times 10$
$ = \dfrac{{537}}{{10}} \times \dfrac{{10}}{1}$
$ = \dfrac{{5370}}{{10}}$
Now, we have to reduce the fraction to its lowest terms.
We have a common number $10$ in both the numerator and denominator of the fraction.
$\dfrac{{10 \times 537}}{{10}}$
$ = \dfrac{{537}}{1}$
$ = 537$
Hence, the required value of the product $53.7 \times 10$ is $537$.

Note: One should be well acquainted with the conversion of decimal into a fraction and vice versa to conduct all the operations. We can also reduce the number of steps by canceling the common term $10$ in the initial steps without the need of multiplying the numerator and denominator at the beginning. Instead of reducing the terms at the end, we can cancel out the terms initially to make the calculations simpler.