Estimating Worksheets | Questions and Revision | MME

Estimating Worksheets, Questions and Revision

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What you need to know

Estimating

The way we estimate answers to calculations is simple – we round every number involved to 1 significant figure, and then calculate with those numbers instead. Just to recall, we start counting significant figures from the first non-zero digit. For some more practise on rounding numbers take a look over here .

In the higher course only, you may also be asked about a slightly different types of estimation, and that is estimating powers and roots. When estimating powers, we can take the same approach e.g. to estimate (9.306)^2, we can round 9.306 to 9, and then work out the estimate to be 9^2 = 81.

Example 1: Simple Estimating

Estimate the answer to \dfrac{8.21}{3.97} \times 31.59.

Round each number to 1 significant figure:

8.21 \text{ rounds to } 8,

3.97 \text{ rounds to } 4,

31.59 \text{ rounds to } 30.

Therefore, we get

\dfrac{8.21}{3.97} \times 31.59 \approx \dfrac{8}{4} \times 30 = 2 \times 30 = 60.

So, the estimate answer to the calculation is 60 (compared to real answer of 65.328… it’s not too shabby).The \approx symbol means “approximately equal to”.

Example 2: Estimating with Equations

The formula for the force, F on a moving object is F = ma, where m is the mass and a is the acceleration. Estimate the force on an object which has mass 5.87\text{ kg} and acceleration 24.02\text{m/s}^2.

Round the numbers in the question to 1 significant figure:

5.87 \text{ rounds to } 6,

24.02 \text{ rounds to } 20.

Therefore, we get

\text{Force } = 5.87 \times 24.02 \approx 6 \times 20 = 120

Example 3: Estimating Square Roots

Find an estimate for \sqrt{40}.

The square root of 40 will be some number that we can square to make 40. We know that

6^2 = 36 \text{ and } 7^2 = 49

So, the answer must fall somewhere between 6 and 7. Since 40 is 4 away from 36 but 9 away from 49, we can conclude the answer will be somewhat closer to 6.

Therefore, 6.3 is the estimate for \sqrt{40}.

Example Questions

Round each number to 1 significant figure:

 

9.02 \text{ rounds to } 9,

 6.65 \text{ rounds to } 7

0.042 \text{ rounds to } 0.04

11 \text{ rounds to } 10.

 

Therefore we get, 

 

\dfrac{9.02 + 6.65}{0.042 \times 11} \approx \dfrac{9 + 7}{0.04 \times 10} = \dfrac{16}{0.4}

 

To make this division easier, multiply the top and bottom of the fraction by ten, to find

 

\dfrac{16}{0.4} = \dfrac{160}{4} = 40

Rounding each number to 1 significant figure:

 

57.33\textrm{ rounds to }60
29.88\textrm{ rounds to }30
8.66\textrm{ rounds to }9
5.55\textrm{ rounds to }6

Therefore, we get:

 

\dfrac{57.33-29.88}{8.66-5.55}\approx\dfrac{60-30}{9-6}=\dfrac{30}{3}=10

Because the answer needs to be in pounds, we should turn the cost of the pencils into pounds first.

45p=\pounds0.45

Now we can start estimating.

1.89\textrm{ rounds to }2
0.45\textrm{ rounds to }0.5

 

And now we need to multiply these amounts by how many of each he wanted.

 

\textrm{(Pens) }\pounds2\times5=\pounds10
\textrm{(Pencils) }\pounds0.50\times3=\pounds1.50

 

And now all we need to do is add them together.

 

\pounds10+\pounds1.50=\pounds11.50

Round each number to 1 significant figure:

 

32.60 \text{ rounds to } 30,

 

17.50 \text{ rounds to } 20,

 

Therefore, the approximate cost of the 3 child tickets is 3 \times 20 = \pounds 60.

 

The approximate cost of the 2 adult tickets is 2 \times 30 = \pounds 60.

 

Thus, the approximate total cost is 60 + 60 = \pounds 120.

Round the number to 1 significant figure,

98\approx100 

 

Therefore,

\sqrt{98}\approx\sqrt{100}=10

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