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 \pi, knowing it's not exactly right but close enough.

Example 1

easy
Estimate \sqrt{50} to one decimal place without a calculator.

Example 2

medium
Use the approximation \pi \approx \dfrac{22}{7} to estimate the circumference and area of a circle with radius 14 cm. Compare with the decimal approximation \pi \approx 3.14159.

Example 3

easy
Estimate 198 \times 52 using rounding, then compute the exact answer and find the percent error.

Example 4

medium
Use the first-order linear approximation \sqrt{a+\epsilon} \approx \sqrt{a} + \dfrac{\epsilon}{2\sqrt{a}} to estimate \sqrt{101}.