Chapter 0, Problem 31P

To determine

To find: the quotient of the given number

Answer to Problem 31P

The required division is $\mathrm{294.212963.}$

Explanation of Solution

Given: $2542÷864$

Calculation:

Thus, multiply both divisor and dividend by 100 to make a whole number.

  $254200÷864$

Now, performing division

  $\begin{array}{l}\text{ 294}\text{.21296296}\\ 864)\overline{\text{254200 }}\\ \underset{\_}{\text{-1728 }}\\ \text{ 8140}\\ \underset{\_}{\text{ -7776 }}\\ \text{ 3640}\\ \underset{\_}{\text{ - 3456 }}\\ \text{ 1840}\\ \underset{\_}{\text{ - 1728 }}\\ \text{ 1120}\\ \underset{\_}{-\text{ 864 }}\\ \text{ 2560}\\ \underset{\_}{\text{ - 1728 }}\\ \text{ 8320}\\ \underset{\_}{\text{- 7776 }}\\ \text{ 5440}\\ \underset{\_}{\text{- 5184 }}\\ \text{ 2560}\\ \underset{\_}{\text{- 1728 }}\\ \text{ 8320}\\ \underset{\_}{\text{- 7776 }}\\ \text{ 5440}\\ \underset{\_}{\text{- 5184 }}\\ \text{ 2560}\end{array}$

Here, the quotient is repeating itself after $294.21296,$ with 296 being repeated part. These types of decimals are known as recurring decimals. And quotient is written as $294.21296$

Conclusion:

Thus, the required division is $\mathrm{294.212963.}$