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

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Simon Thomas 6 years, 1 month ago

Created this as a copy of Q7 (Calculate the estimate, actual and from these the percentage error).

Name	Status	Author	Last Modified
Q9 (Percentage error in area of circle)	draft	TEAME CIT	11/10/2016 22:42
Q11 & 12 (Percentage Error with multipling and rounding-off)	draft	TEAME CIT	11/10/2016 22:47
Q1 (Percentage Error)	draft	TEAME CIT	07/10/2016 23:19
Q4 (Percentage error when estimating total cost of shop items)	draft	TEAME CIT	07/10/2016 23:18
Q5 percentage error	draft	TEAME CIT	08/10/2016 19:57
Q6 (Calculate the minimum and maximum approximations of an estimate)	draft	TEAME CIT	08/10/2016 19:57
Q7 (Calculate the estimate, actual and from these the percentage error)	draft	TEAME CIT	08/10/2016 19:58
Q8 (Calculate the estimate, actual and the percentage error from these)	draft	TEAME CIT	08/10/2016 19:58
Simon's copy of Q1 (Percentage Error)	draft	Simon Thomas	20/02/2019 11:19
Simon's copy of Q4 (Percentage error when estimating total cost of shop items)	draft	Simon Thomas	20/02/2019 11:53
Simon's copy of Q5 percentage error	draft	Simon Thomas	20/02/2019 11:58
Simon's copy of Q6 (Calculate the minimum and maximum approximations of an estimate)	draft	Simon Thomas	20/02/2019 12:09
Simon's copy of Q7 (Calculate the estimate, actual and from these the percentage error)	draft	Simon Thomas	20/02/2019 12:34
Simon's copy of Q8 (Calculate the estimate, actual and the percentage error from these)	draft	Simon Thomas	20/02/2019 11:35

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Question statement

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.

Give any introductory information the student needs.

			Name	Type	Generated Value

num1	integer	546
num2	integer	564
num3	number	47
num4	integer	54
num5	number	122.27
num7	number	60.44
num6	number	26.47
num8	number	38.8
num9	number	58.2
num10	number	21.8
num11	number	49.1
num12	number	7.98
num13	number	3.88
num14	number	18.53
num15	integer	331
num16	integer	281
num17	integer	57
num18	integer	285
num19	number	3.61
num20	number	55.27
num21	number	853.9
ans11	number	120
ans21	number	2.1666666667
ans31	number	120
ans41	number	1.75
ans51	number	0
ans61	number	1.0666666667
ans12	number	121.3333333333
ans22	number	2.4609530113
ans32	number	103.5853211009
ans42	number	1.8348951361
ans52	rational	25/171
ans62	number	0.8435228563
ans13	number	1.0989010989
ans23	number	11.9582268836
ans33	number	15.8465299182
ans43	number	4.6267023346
ans53	decimal	dec("100")
ans63	number	26.4537953764

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Value

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hun()

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

546

This variable doesn't seem to be used anywhere.

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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

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

Estimate (4dp): Gap 0.

Actual (4dp): Gap 1.

% Error (1dp): Gap 2.%

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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This question is used in the following exam:

Error & Approximation by Simon Thomas in Maths support.

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

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`