Question

the number 2.525252.... can be written as a fraction, when reduced to its lowest term, the sum of numerator and denominator is:

Answer 1

349

Explanation:

• 2.525252.... is a non-terminating and recurring number.

• 2.525252.... can be expressed as
  `2.\overline {52}`

• Now, we convert
  `2.\overline {52}` as a fractional number. Lets start.

• 
  `Let \: x =2.\overline {52}`........(1)

• Multiply both sides of eq (1) by 100, we find:

• 
  `100x =252.\overline {52}`........(2)

• Subtracting (2) from (1)

• 
  `100x -x=252.\overline {52}-2.\overline {52}`

• 
  `\implies 99x=250`

• 
  `\implies x=(250)/(99)`

• Numerator = 250

• Denominator = 99

• Sum of numerator and denominator = 250 + 99 = 349

Answer 2

Here's your answer.

Let the number be x.

Here we have to multiply with 100 on both sides.

`\implies \: 100x = 252.5252 \\ \\ \implies \: 100x = 250 \ + 2.5252... \\ \\ \implies \: 100x = 250 + x \\ \\ \implies \: 99x = 250 \\ \\ \implies \: x = (250)/(99)`

Therefore, sum of numerator and denominator = 25099 = 349

Hope it helps you from my side