Question

Which decimal is the best estimate of the fraction 29\40?

Answer 1

`(29)/(40)=0.725`

Solution

We are asked to find the best estimate for the fraction:

`(29)/(40)`

- The easiest way to evaluate this fraction is to separate the denominator into 4 and 10 and then divide 29 by 4. The result of the division can then be divided by 10.

- This is done below:

`\begin{gathered} (29)/(40)=(29)/(4*10)=(29)/(4)*(1)/(10) \\ \\ =7(1)/(4)*(1)/(10)=7(1)/(4)*0.1 \\ \\ \text{But }(1)/(4)=0.25 \\ \\ 7(1)/(4)=7+0.25=7.25 \\ \\ =7.25*0.1=0.725 \\ \\ \therefore(29)/(40)=0.725 \end{gathered}`

Final Answer

`(29)/(40)=0.725`