Question

If x has been measured as 5.0 ± 0.05 cm, what should we report for 2x^2 and x^3/2?

Answer 1

When x is measured as 5.0 ± 0.05 cm, we report 50.0 and 11.2 for
`2x^2` and
`x^3^/^2` respectively.

Step-by-step explanation:

When we have a measured value with uncertainty, we should report our final answer with the same number of decimal places as the value with the least number of decimal places in the uncertainty. In this case, the measured value is 5.0 cm with an uncertainty of 0.05 cm, which has 1 decimal place. Therefore, our final answers for
`2x^2` and
`x^3^/^2` should also have 1 decimal place.

For
`2x^2`, we substitute the value of x into the expression and square it.

So
`(2x^2)` =
`2(5.0)^2`

= 2(25.0)

= 50.0.

Since 50.0 has 1 decimal place, we report the answer as 50.0.

For
`x^3^/^2`, we cube the value of x and take the square root of the result.

So
`(x^3^/^2^)` =
`(5.0^3)^(^1^/^2^)`

=
`125.0^(^1^/^2^)`

= 11.2.

Since 11.2 also has 1 decimal place, we report the answer as 11.2.