Question

How do you convert $\dfrac{1}{8}$ to a decimal using long division?

Answer 1

Hint: First to convert $\dfrac{1}{8}$ to a decimal using long division, we need to set up the number in the long division form and then evaluate by placing a decimal point in the quotient as we add zeros in the dividend. Solve it till we get the remainder zero in this method. The decimal value which we get in the quotient will be the answer.

Complete step-by-step solution:
We are asked to find the decimal value of $\dfrac{1}{8}$ using a long division method.
A piece of essential arithmetic, long division is a technique for tackling and finding the appropriate response and remaining portion for division issues that include numbers with at any rate two digits. Learning the essential strides of long division will permit you to separate quantities of any length, including both whole numbers and decimals.
First let us set up the division form.
$8\overline{\left){1}\right.}$
The basic rule to find the quotient for a dividend lesser than the divisor is that,
When we add zeros to the dividend, we add a decimal point and then solve for it in the quotient.
We get,
$8\overset{0.}{\overline{\left){10}\right.}}$
Now let us start solving.
$8\overset{0.1}{\overline{\left){\begin{align}
  & 10 \\
 & -8 \\
 & \overline{\left){2}\right.} \\
\end{align}}\right.}}$
Now again add a zero in the dividend.
Do not worry about the quotient because we have already placed a decimal point and we can add as many zeroes required in the dividend.
$8\overset{0.12}{\overline{\left){\begin{align}
  & 10 \\
 & -8 \\
 & 8\overline{\left){\begin{align}
  & 20 \\
 & -16 \\
 & \overline{\left){4}\right.} \\
\end{align}}\right.} \\
\end{align}}\right.}}$
Now again add a zero in the dividend since dividend is lesser than the divisor.
$8\overset{0.125}{\overline{\left){\begin{align}
  & 10 \\
 & -8 \\
 & 8\overline{\left){\begin{align}
  & 20 \\
 & -16 \\
 & 8\overline{\left){\begin{align}
  & 40 \\
 & -40 \\
 & 0 \\
\end{align}}\right.} \\
\end{align}}\right.} \\
\end{align}}\right.}}$
Hence upon converting $\dfrac{1}{8}$ to a decimal using long division we get the value as 0.125

Note: Always check the number of decimal places (number of digits) after the decimal place to convert the decimal into a fraction. The number of digits is then written to the power of $10$ and then placed in the denominator and in the numerator, the number will be written the same as it is, but without the decimal point.