Question

How do you simplify and make the decimal \[0.875\] into a fraction?

Answer 1

Hint: In this question we want to convert a decimal number to a fraction. First, we will remove all the decimal numbers by dividing and multiplying the decimal number by $10$, and then we will simplify the fraction to get the simplest form of the fraction.

Complete step by step answer:
For converting a decimal number to a fraction, we will follow the given steps:
First step: the decimal number is rewritten in the form of a fraction. The decimal number comes in the numerator and in the denominator write\[1\].
Second step: multiply both numerator and denominator with \[10\]and it is repeated up to when the decimal point is reached in the end. (and also we calculate direct as if there is one digit after decimal point then multiply both numerator and denominator with ten if there is two-digit after decimal point then multiply both numerator and denominator with hundred and if it is three-digit after decimal point then we multiply both the numerator and denominator with thousand).
Third step: then calculate the simplest form from fraction.
In the question the decimal number is given that \[ = 0.875\]
For converting in fraction form we want to write \[1\] in the denominator. And
Then,
The fraction form is given below.
\[ \Rightarrow \dfrac{{0.875}}{1}\]
In the fraction form, we want to multiply with \[10\]in both numerator and denominator.
Then the new fraction form is come as below:
\[ \Rightarrow \dfrac{{8.75}}{{10}}\]
Now we will check that the decimal point is reached in the end or not, if not then multiply again by \[10\]in both numerator and denominator.
Then, the new form comes as below.
\[ \Rightarrow \dfrac{{87.5}}{{100}}\]
Again, repeat the step to check if a decimal point is reached in the end or not, if not then multiply with \[10\]in both numerator and denominator.
Then,
\[ \Rightarrow \dfrac{{875}}{{1000}}\]
Now, we check that the decimal point is reached in the end, if the answer is yes then come to the next step and express in simplest form.
Then,
In the form of a fraction, \[25\]is common in both numerator and denominator. Then we divided both with\[25\].
Then,
\[ \Rightarrow \dfrac{{875/25}}{{1000/25}}\]
The new result comes as below.
\[ \Rightarrow \dfrac{{35}}{{40}}\]
In the above form of a fraction, \[5\] is common in both numerator and denominator. Then we divided both with\[5\].
Then,
\[ \Rightarrow \dfrac{{35/5}}{{40/5}}\]
The new form of fraction is-
\[\therefore \dfrac{7}{8}\]

Therefore, the fraction of a decimal number \[0.875\] is \[\dfrac{7}{8}\].

Note: As we know that if a decimal number is given and want to convert is fraction form then we assume the \[1\] in the denominator. And multiply both numerator and denominator with\[10\], it is repeated up to when the decimal number is reached in the end.