Question

How do you convert $\dfrac{1}{4}$ into a percent and a decimal?

Answer 1

Hint: For the given fraction, to convert it both into a decimal and a fraction, we multiply the numerator and the denominator by $100$ . The division by $100$ can be expressed as $0.01$ for a decimal, and as $\%$ for a percent.

Complete step by step solution:
The given fraction is
$\dfrac{1}{4}$
To convert a proper fraction into a decimal, we need to make it an improper fraction at first. This can be done by multiplying the numerator and denominator by a number, but keeping the number separate which is multiplied in the denominator. The new numerator must be exactly divisible in the previous denominator in this case. In other words, let us multiply the numerator and the denominator by $100$ . The fraction thus becomes,
$\Rightarrow \dfrac{1\times 100}{4\times 100}=\left( \dfrac{100}{4} \right)\times \dfrac{1}{100}$
Decimals are defined by division by $10$ and its multiples. So, $0.1$ means $\dfrac{1}{10}$ , $0.01$ means $\dfrac{1}{100}$ and so on. The fraction can thus be written as,
$\Rightarrow \left( \dfrac{100}{4} \right)\times \dfrac{1}{100}=\left( \dfrac{100}{4} \right)\times 0.01$
$100$ upon division by $4$ gives the quotient as $25$ and no remainder. Thus, the above fraction can be written as,
$\Rightarrow \left( \dfrac{100}{4} \right)\times 0.01=25\times 0.01$
$25$ times $0.01$ means $0.25$ . Thus, the number becomes,
$\Rightarrow 0.25$
Now, percent means “out of $100$ “. For this, we need to multiply the numerator and denominator by $100$ itself, but keeping the $100$ separate which is multiplied in the denominator. The fraction thus becomes,
$\Rightarrow \dfrac{1\times 100}{4\times 100}=\left( \dfrac{100}{4} \right)\times \dfrac{1}{100}$
Here, instead of writing or expressing the $\dfrac{1}{100}$ term as $0.01$ , we express it as $\%$ . The expression thus becomes,
$\Rightarrow \left( \dfrac{100}{4} \right)\times \dfrac{1}{100}=\left( \dfrac{100}{4} \right)\%$
$100$ upon division by $4$ gives the quotient as $25$ and no remainder. Thus, the above fraction can be written as,
$\Rightarrow \left( \dfrac{100}{4} \right)\%=25\%$
Therefore, we can conclude that the fraction $\dfrac{1}{4}$ can be written $0.25$ as a decimal and $25\%$ as a percent.

Note: While converting into a decimal, we should remember the number of decimal places that we take. Any more or any less of a decimal place can make the answer wrong. To express it as a percent, we can also simply multiply the fraction by $100\%$ to get the answer.