Power of Maths: Paper 1 – Section 1
The mid-value = 45·8 + 46·2 __________
2
= 92·0 ____
2 Tolerance level = (46 ± 0⋅2) mm
Since no measurement is exact, a measurement is quoted with a tolerance level that gives the range within which the true value lies. The temperature of a boiling liquid measured as (78⋅6 ± 0⋅2) °C means that the true value lies between 78⋅4 °C and 78⋅8 °C.
ACTION ACTIVITY
ACTION
Understanding errors
OBJECTIVE To understand how errors accumulate when results are added and subtracted
EXAMPLE 8
A weighing scales can measure the mass of objects to an accuracy of ± 0·002 g. The mass of a beaker is measured as 42·056 g. The mass of the beaker with a copper sulfate solution is measured as 42·863 g. What is the possible range of values of the mass of the copper sulfate solution?
Solution Mass of beaker = (42⋅056 ± 0⋅002) g
Mass of beaker plus copper sulfate solution = (42⋅863 ± 0⋅002) g Mass of copper sulfate solution = (0⋅807 ± 0⋅004) g
The true value of the mass of copper sulfate solution lies in the range = 0⋅803 g to 0⋅811 g
Absolute and percentage error WORKED EXAMPLE Understanding absolute and percentage errors
A 750 g box of cornfl akes in a consignment of food is weighed by Customs. It is found to have a mass of 820 g. The accepted mass of the box of cornfl akes = 750 g The measured mass = 820 g The absolute error =
The percentage error =
| 820 g – 750 g 70 g
| = 70 g
_____ 750 g × 100 % = 9 1
_ 3 %
Do you think that Customs will suspect that the box of cornfl akes is concealing something? Absolute error in a quantity =
Percentage error in a quantity = 38
______________________ Accepted value of quantity × 100 %
Y 11
Experimental results and the accumulation of errors
When the results of a measurement are added or subtracted, their errors always accumulate (add).
A metre stick is used to measure the length of a wooden plank. The plank is longer than 1 m so two measurements must be made.
The fi rst measured length is (96⋅0 ± 0⋅1) cm and the remaining length is (13⋅0 ± 0⋅1) cm. The total length of the plank is (109 ± 0⋅2) cm.
Even when you subtract two measurements, their errors add.
= 46
| Measured value of quantity – Accepted value of quantity Absolute error in quantity
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