Practice Approximation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A value intentionally chosen to be close to but not exactly equal to the true value, with a known or estimated error.
We use 3.14 for , knowing it's not exactly right but close enough.
Showing a random 20 of 50 problems.
Example 1
mediumCompute the percent error when is approximated as (use the true value ).
Example 2
mediumUse the first-order linear approximation to estimate .
Example 3
easyRound to two decimal places.
Example 4
hardA circular table has measured diameter m (with m uncertainty). Approximate its area and its uncertainty.
Example 5
easyEstimate using rounding, then compute the exact answer and find the percent error.
Example 6
easyEstimate to one decimal place without a calculator.
Example 7
challengeEstimate and use one Newton step to improve it.
Example 8
mediumUse the approximation to estimate the circumference and area of a circle with radius cm. Compare with the decimal approximation .
Example 9
mediumTo estimate between consecutive tenths, which two values bracket it?
Example 10
easyTrue or false: every approximation has some error.
Example 11
easyRound to two decimal places.
Example 12
mediumA budget of is rounded to for a report. What is the rounding error, and is it an over- or under-estimate?
Example 13
challengeA surveyor estimates a hill's height using the angle of elevation. If the measured angle is and the horizontal distance is m (exact), give the approximate height and its uncertainty.
Example 14
easyEstimate to decimal place.
Example 15
mediumApproximate to the nearest hundred.
Example 16
hardUse the linear approximation for small to estimate .
Example 17
easyApproximate to the nearest whole number.
Example 18
easyApproximate as a decimal to two places.
Example 19
hardWhat is the relative error if a measurement of kg is off by kg?
Example 20
easyRound to the nearest hundred.