Question

What is $\dfrac{1}{10}$ the value of $0.1$ ?

Answer 1

Hint: We first count the number of decimal digits and then convert it into fraction accordingly. The corresponding fraction is $\dfrac{1}{10}$ . Now, “of” in arithmetic means multiplication. So, the answer will be the one after multiplying $\dfrac{1}{10}$ with $\dfrac{1}{10}$ .

Complete step-by-step answer:
Fractions are a way to define divisions. For example, $\dfrac{1}{2}$ means division of $1$ by $2$ . The number above the bar is called the numerator and the number below it is called denominator. Fractions are of various types like, proper fraction (where the numerator is smaller than the denominator), improper fraction (where the denominator is smaller than the numerator), and so on. Decimals also represent divisions, but consider the divisions to be divided by multiples of $10$ . Decimals also denote the same thing but in a different format; in place of bar, it uses a point with numbers lying on the left and right sides of it.
Decimal to fraction conversion or fraction to decimal conversion is very easy. In decimals, we count the number of digits after the decimal point. The number of digits denotes the power of $10$ which divided the original number and transformed it to a decimal. In this problem, we are given the number as $0.198$ . The number of digits after the decimal point are $3$ . So, the power of $10$ will be $3$ . That means, if we want to remove the decimal point, we have to replace it with “division by ${{10}^{3}}$ “. The decimal thus becomes,
$0.1=\dfrac{1}{10}$
$\dfrac{1}{10}$ of the decimal will then be $\dfrac{1}{10}\times \dfrac{1}{10}=\dfrac{1}{100}=0.01$ .

Note: We can also solve the problem in another way. We do not convert the decimal into fraction. Instead, we convert the fraction into decimal as $\dfrac{1}{10}=0.1$ . Now, we multiply the two decimals $0.1$ to get $0.1\times 0.1=0.01$ .