Question

How do you turn $\dfrac{7}{8}$ into a decimal and percent?

Answer 1

Hint: It is always better to look at the denominator first when we need to convert a fraction into decimal. If the denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of 10 and the result will be a limiting decimal. In case it has a prime factor other than $2$ and $5$, conversion to decimal could be longer and will result in an infinite loop with repeating decimals.
To convert a fraction into percent, it is always better to look at the denominator first. A percentage is written in a specific format where the bottom number (denominator) is 'fixed' at $100$. To convert the fraction to percent, one needs to just multiply the value $100$ and write $\% $ sign against the result.

Complete step-by-step answer:
 According to given information, we need to turn $\dfrac{7}{8}$ into decimal.
As the only prime factor of the denominator which is $8$is $2$.
In fact there are three twos ($2 \times 2 \times 2$) , i.e., $(8) = 2 \times 2 \times 2$.
Further, we can convert the fraction $\dfrac{7}{8}$ by multiplying numerator and denominator by $5 \times 5 \times 5$into $1000$, which is a power of $10$.
$\dfrac{7}{8} = \dfrac{{7 \times 5 \times 5 \times 5}}{{8 \times 5 \times 5 \times 5}} = \dfrac{{875}}{{1000}} = 0.875$
Therefore, we get that $\dfrac{7}{8}$ can be written as $0.875$ in a decimal form.
According to the given data, we need to write $\dfrac{7}{8}$ as a percent.
As we move forward, we can rewrite this as,
$\dfrac{7}{8} = \dfrac{x}{{100}}$
$ \Rightarrow \dfrac{7}{8} \times 100 = 100 \times \dfrac{x}{{100}}$
$ \Rightarrow x = \dfrac{{700}}{8}$
We finally get $x = 87.5$.
Therefore, $\dfrac{7}{8}$can be written as $87.5\% $.

Note: It is always better to look at the denominator first when we need to convert a fraction into decimal. If a denominator only has $2$ and $5$ as prime factors, one can easily select a number which when multiplied to the denominator converts the denominator, in a power of $10$ . This is always possible if only prime factors of denominator are 2's and 5's - just multiply by as many 5's and 2's.
"Percent" or "$\% $" means "out of $100$" or "per $100$". For example, $x\% $ can be written as $\dfrac{x}{{100}}$. To convert the fraction to percent, one needs to just multiply the value $100$ and write $\% $ sign against the result.