Chapter P, Problem 12RE

Solution

Write the given number in decimal form, and state whether it repeats or terminates.

  $-\frac{5}{11}=-\mathrm{0.454545....}$

And it is a repeating decimal.

Given information:

The given number is:

  $-\frac{5}{11}$

Formula used:

1. Decimal form of a number consists of a whole number and a fractional part separated by decimal (.) point. There is no multiplication by the power of 10(or any other number) in it.
2. A terminating decimal is a number that has end.
3. A repeating decimal is recurring decimal in which digits keep on repeating after a fixed interval after decimal.

Calculation:

In order to write the given number

  $-\frac{5}{11}$

in decimal form write it as a whole number and fractional part separated by decimal point.

Since, the given number is a fraction so simplify it by dividing 5 by 11 as

  

Note from the above division it can be seen that after few terms the terms are repeating, i.e it can be written as:

  $-\frac{5}{11}=-\mathrm{0.454545....}$

Thus, the decimal form of given number is:

  $-\frac{5}{11}=-\mathrm{0.454545....}$

And it is a repeating decimal.