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Question

                     __

Express 0.225(recurring decimal 25) as a rational no. Using concepts of periods and periodicity.


Solution

above solution is correct
There are three digits in the decimal 0.225, so the last digit is the 1000ths place. This shows that 0.225 = 225/1000.

The fraction 225/1000 is not in its simplest form. To reduce the fraction, find the Greatest Common Divisor (GCD) / Greatest Common Factor (GCF).  We can reduce this fraction to its lowest terms by dividing the numerator and denominator by 25 because it is the GCD/GCF.

So now, divide 225 and 1000 by 25...

The final answer is 9/40.


Mathematics

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