Calculation Estimation

Warm up:

Significant figure rounding

Linear Interpolation

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How to Estimate of Calculations:

Firstly round all numbers in the calculation to one significant, then proceed with mental calculation until you have your final estimated value of the calculation.

Example:

$$\frac{\left(\frac{19.87-0.01+\frac{0.87}{125}}{17.468}\right)\times 37.924-\sqrt{111}}{0.377-1.9}$$

Rounding all numbers to one significant figure:

$$\frac{\left(\frac{20-0.01+\frac{0.9}{100}}{20}\right)\times 40-\sqrt{100}}{0.4-2}$$ $$=\frac{\left(\frac{20}{20}\right)\times 40-10}{-1.6}$$ $$=\frac{1\times 40-10}{-1.6}$$ $$=\frac{30}{-1.6}$$ $$\approx -20$$

A calculator gives an answer of $-21.40290341$, so our estimate is only 7% away from the accurate answer.

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Exercises:

Estimate the answers to these questions.

1. $3.1\times 7.2$

2. $47.9\times 12.1$

3. $394.82\times 15.9$

4. $78.1\times 1239.32$

5. $79.868÷0.24$

6. $0.101÷23.2$

7. $315.71÷7.8$

8. $0.53÷24.1$

9. $(5.1+17.9)\times 20.92$

10. $(19.6\times 8.3)÷0.11$

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Additional Material:

Number: estimation

Practice Questions

Textbook Exercise

Sensible estimates

Practice Questions

Textbook Exercise

(Care of corbettmaths.com)

Estimating

Exam Questions

Estimation

Solutions

(Care of www.mathsgenie.co.uk)

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See also

Angles: estimation

Practice Questions

Textbook Exercise

Averages: mean (estimated)

Practice Questions

Textbook Exercise

(Care of corbettmaths.com)

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Follow on Material

Fermi Estimates

Limits of Accuracy

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Limits of Accuracy

Limits of Accuracy
(Care of corbettmaths.com)

Bounds
(Care of www.piximaths.co.uk)

Understanding Accuracy in Maths
(Care of revisionmaths.com)