Question

Suppose we approximate the value of 1/128 by rounding to 3 decimal places. a) What would be the approximation? b) What is the number of significant digits in the approximation? c) What is the absolute error? d) What is the relative error?

Answer 1

solved

Explanation:

Calculating i found the value of
`(1)/(128)`= 0.0078125

a.therefore the approximate valve of
`(1)/(128)` (correct to three decimal places) = 0.008

b. there are three significant digits in my approximation.

c. the absolute error = | exact value- approximate value |

=|0.0078125- 0.008|= |-0.0001875| = 0.0001875

d.relative error=
`( absolute\ error)/(exact\ value)`

=
`(0.0001875)/(0.0078125)`= 0.024