Units Of Measurement And Applications Worksheet Page 15
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44Greatest possible error and percentage error
The rod in question 5 h as been measured to the nearest centimetre because this is the smallest unit on the ruler:
the length is closer to 14 cm than to 13 cm or 15 cm. The greatest possible error is 0.5 cm or half of the smallest
scale (cm) on the ruler.
The actual length will lie between 13.5 cm and 14.5 cm; that is, between 14 − 0.5 cm and 14 + 0.5 cm. To obtain
a more accurate measurement, we would need to use a more accurate ruler, one that has smaller units on it.
The smallest unit on a measuring instrument is called the limit of reading of the instrument.
The greatest possible error (GPE) in measuring a quantity (sometimes called the absolute error) is equal
to half the limit of reading.
The smallest and largest values between which the actual measurement lies are called the lower and upper
limits of the true measurement.
As there is always some degree of error in a numerical value found by measurement, it follows that the results of
any calculations involving this value will also contain a degree of error.
WORKED EXAMPLE 2
For each of the measurements below, fi nd:
i
the smallest unit of measurement (the limit of reading)
ii
the greatest possible error (GPE).
a
b
18 cm
2.4 kg
Solve
Think
Apply
a
i
The smallest unit of
The last signifi cant fi gure of the
The position of the last
measurement is 1 cm; that is,
number is in the units column. Hence,
digit in the number
the measurement has been
the smallest scale on the measuring
determines the smallest
made to the nearest centimetre.
instrument is 1 cm; that is, the
scale on the measuring
Hence:
measurement has been made to the
instrument used. This
Limit of reading = 1 cm
nearest centimetre, the limit of reading.
is the limit of reading
of the instrument. The
1 _
1 _
GPE =
× 1 cm = 0.5 cm
GPE =
× limit of reading
ii
2
2
greatest possible error
b i
The smallest unit of
The last signifi cant fi gure of the
is half the limit of
measurement is 0.1 kg; that
number is in the tenths column. Hence,
reading.
is, the measurement has been
the smallest scale on the measuring
made to the nearest 0.1 of a
instrument is 0.1 kg; the measurement
kilogram. Hence:
has been made to the nearest 0.1 of a
Limit of reading = 0.1 kg
kilogram. This is the limit of reading.
1 _
1 _
GPE =
× 0.1 kg = 0.05 kg
GPE =
× limit of reading
ii
2
2
6
Complete the following.
a
For a measurement given as 138 cm, t he last signifi cant fi gure is in the ____ column.
Hence, the smallest scale on the measuring instrument is ____ .
T he measurement has been made to the nearest ____.
Hence, the limit of reading = ____ .
1 _
GPE =
× ____ = ____
2
Chapter 2
Units of measurement and applications
49
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