Name ________________ Date _________ Block__
Accuracy/Sig Figs/ Uncertainties
Topic 1.2.6-10
1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures
 The numbers reported in a measurement are limited by the ___________ tool
 Significant figures in a measurement include the known digits plus one estimated digit
 The number of sig figs should reflect the precision of the value of the input data.
 If the precision of the measuring instrument is not known then as a general rule, give your answer to 3 sig
figs.
Three Basic Rules
 Non-zero digits are always significant.
 523.7 has ____ significant figures
 Any zeros between two significant digits are significant.
 23.07 has ____ significant figures
 A final zero or trailing zeros if it has a decimal, ONLY, are significant.
 3.200 has ____ significant figures
 200 has ____ significant figures
 How many sig. fig’s do the following numbers have?
 38.15 cm _________
5.6 ft ____________
2001 min ________ 50.8 mm _________
 25,000 in ________
200. yr __________
0.008 mm ________ 0.0156 oz ________
Exact Numbers
 Can be thought of as having an ___________ number of significant figures
 An exact number won’t limit the math.
 12 items in a dozen
 12 inches in a foot
 60 seconds in a minute
Multiplying and Dividing
 Round to so that you have the same number of significant figures as the measurement with the
___________ significant figures.
42
two sig figs
x 10.8 three sig figs
453.6
answer
450 two sig figs
 In each calculation, round the answer to the correct number of significant figures.
A. 2.19 X 4.2 =
B. 4.311 ÷ 0.07 =
Adding and Subtracting
 Base your answer on which number column is ___________ significance.
25
+ 1.34
26.34 Calculated Answer
26 Rounded answer based on sig figs
 In each calculation, round the answer to the correct number of significant figures.
A. 235.05 + 19.6 + 2.1 =
B. 58.925 - 18.2 =
1.2.9 Calculate quantities and results of calculations to the appropriate number of significant figures
Practice
 How many sig figs are in each number listed?
 A) 10.47020
D) 0.060
 B) 1.4030
E) 90210
 C) 1000
F) 0.03020
 Calculate, giving the answer with the correct number of sig figs.
 12.6 x 0.53
 (12.6 x 0.53) – 4.59
 (25.36 – 4.1) ÷ 2.317
1.2.9 Practice 13(Dickinson)
 A meter rule was used to measure the length, height and thickness of a house brick and a digital balance was
used to measure its mass. The following data were obtained. Length = 20.5cm, height = 8.4cm, thickness
10.2cm, mass = 3217.94g Calculate the density of the house brick and give your answer to an appropriate
number of sig figs.
1.2.10 State uncertainties as absolute, fractional and percentage uncertainties.
 ___________ uncertainties(errors) due to the precision of a piece of apparatus can be represented in the
form of an uncertainty range.
 Experimental work requires individuals to judge and record the numerical uncertainty of recorded data and
to propagate this to achieve a statement of uncertainty in the calculated results.
Rule of Thumb
 ___________ instruments = +/- half of the limit of reading
 Ex. Meter stick’s limit of reading is 1mm so it’s uncertainty range is +/- 0.5mm
 Digital instruments = +/- the limit of the reading
 Ex. Digital Stopwatch’s limit of reading is 0.01s so it’s uncertainty range is +/- 0.01s
 We can express this uncertainty in one of three ways- using absolute, fractional, or percentage uncertainties
 Absolute uncertainties are constants associated with a particular measuring device.
 (Ratio) Fractional uncertainty = absolute uncertainty
measurement
 Percentage uncertainties = fractional x 100%
Example
 A meter rule measures a block of wood
 Absolute =
 Fractional = 0.5mm =
28mm
 Percentage = 0.0179 x 100% =
28mm long.
28mm +/- 0.5mm
28mm +/- ___________
28mm +/- ___________