Simon's copy of Q7 (Calculate the estimate, actual and from these the percentage error)

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Question 1

By rounding each number correct to one significant figure, estimate the answer to each of the problems given below, giving your final estimate to 4 d.p.

Then use your calculator to correctly evaluate the exact calculation to 4 d.p.

Calculate the percentage error in using the estimate, correct to one decimal place.

a)

$\frac{\var{num1} \times \var{num2}}{\var{num3} \times \var{num4}}$

Estimate (4dp): Round your answer to 4 decimal places.Expected answer:

Actual (4dp): Round your answer to 4 decimal places.Expected answer:

% Error (1dp): Round your answer to 1 decimal place.Expected answer:%

Score: 0/3

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b)

$\frac{\var{num5} + \var{num6}}{\var{num7}}$

Estimate (4dp): Round your answer to 4 decimal places.Expected answer:

Actual (4dp): Round your answer to 4 decimal places.Expected answer:

% Error (1dp): Round your answer to 1 decimal place.Expected answer:%

Score: 0/3

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c)

$\frac{\var{num8} \times \var{num9}}{\var{num10}}$

Estimate (4dp): Round your answer to 4 decimal places.Expected answer:

Actual (4dp): Round your answer to 4 decimal places.Expected answer:

% Error (1dp): Round your answer to 1 decimal place.Expected answer:%

Score: 0/3

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d)

$\frac{\var{num19}^2 \times \var{num20}}{\var{num21}}$

Estimate (4dp): Round your answer to 4 decimal places.Expected answer:

Actual (4dp): Round your answer to 4 decimal places.Expected answer:

% Error (1dp): Round your answer to 1 decimal place.Expected answer:%

Score: 0/3

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Advice

When rounding off a number to one significant place, round to the left most figure of the number, e.g:

$367 \rightarrow 400$ , $38 \rightarrow 40$ , $71 \rightarrow 70$

$3.79 \rightarrow 4$ , $65.13 \rightarrow 70$ , $0.0215 \rightarrow 0.02$

$0.00465 \rightarrow 0.005$

(a)

Round each number to one significant number:

$\var{num1} \rightarrow \var{siground(num1,1)}$ , $\var{num2} \rightarrow \var{siground(num2,1)}$

$\var{num3} \rightarrow \var{siground(num3,1)}$ , $\var{num4} \rightarrow \var{siground(num4,1)}$

So for our approximation we use:

$\frac{\var{siground(num1,1)} \times \var{siground(num2,1)}}{\var{siground(num3,1)} \times \var{siground(num4,1)}} = \var{precround(ans11,4)}$

remembering to give our answer to 4 d.p. as requested.

The exact value is:

$\frac{(\var{num1} \times \var{num2})}{(\var{num3} \times \var{num4})} = \var{precround(ans12,4)}$

So our percentage error:

$\frac{|\var{precround(ans12,4)} - \var{precround(ans11,4)}|}{\var{precround(ans11,4)}} \times 100 = \var{precround(ans13,1)}$ %

(b),(c),(d) can be completed using a similar method

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Numbas has failed

Simon's copy of Q7 (Calculate the estimate, actual and from these the percentage error)

a)

b)

c)

d)

Advice