Maths Made Easy Forums Standard Measurement Measurement Error

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• A roast is to cook for 1 hour and 30 minutes correct to the nearest 10 minutes. The percentage error is?

accuracy = 10 minutes

error = 5 minutes (ie half the accuracy)

% error =  error/measurement × 100

5/90 × 100 = 5.6%
(don’t forget you have to change the 1 hour 30 mins to minutes only)

• Tom measures a piece of fabric with a ruler that is only marked in centimetres. He measures the length to be 60cm and the width 90cm. The area of the fabric is:  a. between 5399.5cm2 and 5400.5cm2
b. between 5384.75cm2 and 5414.75cm2
c. between 5325.25cm2 and 5475.25cm2
d. between 5251cm2 and 5551cm2

accuracy = 1cm

error = 0.5cm

60 – 0.5 = 59.5

60 + 0.5 = 60.05

90 – 0.5 = 89.5

90 + 0.5 = 90.05

lower area = 59.5 × 89.5

= 5325.25cm2

upper area = 60.5 × 90.5

= 5475.25cm2

∴ C

• A rectangular paddock is 36 metres long and 25 metres wide, measured to the nearest metre. It requires fencing along all sides.
a. Between what two measurements does the length lie?
b. Between what two measurements does the width lie?
c. What is the smallest possible length of fencing needed?
d. What is the largest possible length of fencing needed?
e. What is the maximum percentage error in the length of fencing needed?

a. accuracy = 1m
error = 0.5m
length 36 – 0.5 and 36 + 0.5
35.5m – 36.5m

b. width: 25 – 0.5 and 25 + 0.5
24.5m – 25.5m

c. smallest length of fencing will be the perimeter using the lower limits

P = 35.5 + 24.5 + 35.5 + 24. 5
= 120m

d. largest length of fencing will be the perimeter using the upper  limits
P = 36.5 + 26.5 + 36.5 + 26. 5

= 124m

e. total length of fencing = 36 + 25 + 36 + 25
= 122m

total error = 4 lots of 0.5m
= 2m (since there would be 0.5m per measurement)
% error = $$\frac{2}{122}\times100= 1.6%$$

• A rectangle has a length of 18cm and a width of 12cm.
a. What is the largest possible error?
b. What is the smallest possible area?

a. accuracy = 1cm

error =± 0.5cm

lower limits = 18cm – 0.5cm = 17.5cm
and
12cm – 0.5cm = 11.5cm

upper limits = 18cm + 0.5cm = 15.5cm
and
12cm + 0.5cm = 12.5cm

error =± 0.5cm
b. consider the lower limits = 17.5cm × 11.5cm

= 201.25cm

• Rachel measures her height and finds that she is 171cm tall, to the nearest millimetre, the tallest she can be is:
a. 172.00cm    b. 171.60cm    c. 170.55cm    d. 171.40cm

a will round to 172 b will round to 172 c will round to 171 d will round to 171 so the tallest that will round to 171 is D