Question

How do you write $ 0.187 $ as a fraction in its simplest form?

Answer 1

Hint: For solving the question, we should have some knowledge of multiplication, addition and division as we will be requiring these things in these problems. First, First write down the decimal number divided by 1, and As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by $ {10^3} = 1000 $ , so that there is no decimal point in the numerator.

Complete step-by-step solution:
A fraction is not a whole number but a number in between the whole numbers. It is a part of a whole. Also, a fraction has two parts – a numerator and a denominator.
A decimal number is used to represent a non-whole number where a decimal point is used followed by digits that represent a value that is smaller than one.
Decimals and fractions are different ways of representing the same thing—a number that is not whole.
We can convert a decimal to a fraction by following these three easy steps.
Step One: Rewrite the decimal number over one (as a fraction where the decimal number is a numerator and the denominator is one).
Step Two: Multiply both the numerator and the denominator by 10 to the power of the number of digits after the decimal point. If there is one value after the decimal, multiply by 10, if there are two then multiply by 100, if there are three then multiply by 1,000, etc.
In the case of converting 0.25 to a fraction, there are two digits after the decimal point. Since 10 to the 2nd power is 100, we have to multiply both the numerator and denominator by 100 in step two.
Step Three: Express the fraction in simplest (or reduced form).
When the numerator and the denominator can no longer be reduced to any smaller number separately, we get the fraction in its simplest form.
Example: $ \dfrac{4}{8} $ can be simplified as $ \dfrac{4}{8} = \dfrac{{2 \times 2}}{{2 \times 2 \times 2}} = \dfrac{1}{2} $ ,
In the given example, we obtain the simplified form by dividing the numerator and denominator by 3, the greatest number that divides both the numbers exactly (reducing them into another whole number). Thus, finding the simplest form of a fraction means reducing the top and bottom of the fraction to the smallest whole number possible. The simplest form is the smallest possible equivalent fraction of the number.
Given decimal is $ 0.187 $ ,
First write down the decimal number divided by 1 like this:
 $ \dfrac{{0.187}}{1} $ ,
As we have 3 digits after the decimal point in the numerator, we need to multiply both the numerator and denominator by $ {10^3} = 1000 $ , so that there is no decimal point in the numerator
 $ \Rightarrow \dfrac{{0.187 \times 1000}}{{1000}} $ ,
Now the fraction is,
 $ \Rightarrow \dfrac{{187}}{{1000}} $ ,

The required fraction in its simplified form for the decimal 0.187 is $ \dfrac{{187}}{{1000}} $ .

Note: Fractions and decimals are similar because they both in a way express partial numbers. Just as a decimal can be expressed as a fraction, it can be another way round as well. A fraction can also be converted into a decimal by simply dividing the numerator with the denominator. Also fractions can be expressed as decimals by simply performing the division of the ratio. We can also express decimals as fractions in terms of tenths, hundredths, thousandths, and so on.