Units Of Measurement And Applications Worksheet Page 14
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44WORKED EXAMPLE 1
John measured the width of his maths textbook fi ve times using a ruler marked in millimetres. The results were
190 mm, 189 mm, 190 mm, 192 mm and 190 mm. Average these measurements to give an approximation for
the width of the book, to the nearest millimetre.
Solve
Think
Apply
Average
Determine the average
Averaging measurements reduces
190 + 189 + 190 + 192 + 190
by fi nding the sum of the
the eff ects of any errors. The answer
__________________________
=
5
measurements and then
should be given to the same degree of
= 190.2 mm
dividing by the number of
accuracy as the given measurements
= 190 mm, to the nearest mm
measurements. The answer
(in this case, to the nearest millimetre).
is 190 mm, to nearest mm,
The diff erences in the measurements
as 190.2 is closer to 190
could have been caused by any of the
than to 191.
errors discussed above.
EXERCISE 2E
1
A student measured the length of his textbook using a ruler marked in millimetres. The results were 256 mm,
255 mm, 255 mm, 254 mm and 254 mm. Average these measurements to give an approximation for the length
of the book, to the nearest millimetre.
2
Average the following to give an approximation for the true measurement. In each case, the measurements were
taken to the same degree of accuracy.
a
b
83 mm, 85 mm, 84 mm, 85 mm, 85 mm, 84 mm
4.9 kg, 4.8 kg, 4.9 kg, 5.0 kg, 4.9 kg
c
d
162 mL, 162 mL, 160 mL, 161 mL, 161 mL, 162 mL
22.49 s, 22.61 s, 22.54 s, 22.56 s, 22.52 s
3
Have fi ve students measure your height to the nearest
centimetre. Average these measurements to give an
approximation for your true height.
4
The diagrams show several steel rods being measured with a
ruler divided into centimetres. Write the length of each rod,
using the scale given on the ruler.
a
b
13
14
15
13
14
15
c
d
13
14
15
13
14
15
5
The length of a rod is measured using the ruler in question 4,
and the measurement is recorded as 14 cm.
a
Would this be the exact length of the rod ?
b
Between what values would the actual length lie?
c
What is the greatest possible error in stating that the
length is 14 cm?
d
How could we fi nd a more accurate value of the length of
the rod?
48
Insight Mathematics General 11
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