Mr. Baldwin
Mathematics & Measurement
Aim: Why are significant figures important? (What is
precision and accuracy?)
Do Now: How many seconds are there in a year? Convert you
answer to scientific notation and round it off to 2 decimal
Distinguish between accuracy and precision.
Determine the precision of measured quantities
Significant Figures reviewed
The number of significant figures is the number of reliably
known digits in a number. It is usually possible to tell the
number of significant figures by the way the number is
Some Examples:
23.21 cm has 4 significant figures
0.062 cm has 2 significant figures (the initial zeroes don’t
80 km is ambiguous – it could have 1 or 2 significant
figures. If it has 3, it should be written 80.0 km.
EXAMPLE: A meter-stick is used to measure a pen
and the measurement is recorded as 14.3 cm.
This measurement has three valid digits: two you
are sure of, and one you estimated.
The valid digits in a measurement are called
significant digits.
However, the last digit given for any measurement
is the uncertain digit.
How many significant digits are in these
a) 25.001 cm
b) 0.00012 kg
c) 35,000 m/s
d) 5.611 x 105 s
e) 0.0120 mm
f) 2.00 x 10-3 mL ________
g) 750 dg
Operations Involving Significant Figures
When multiplying or dividing numbers, the result has
as many significant figures as the number used in the
calculation with the fewest significant figures.
Example: 11.3 cm x 6.8 cm = 77 cm
When adding or subtracting, the answer is no more
accurate than the least accurate number used.
Can you create ONE example each of addition and
subtraction involving sig. figs.?
Which of the following representations is correct
when you solve 0.030 kg + 3333 g using scientific
A. 3.4×103 g
B. 3.36×103 g
C. 3×103 g
D. 3363 g
Accuracy & Precision
Define accuracy and precision?
Create two sentences each using the words
precision and accuracy
• Accuracy is the proximity of measurement
results to the true value
• Precision, the repeatability, or reproducibility
of the measurement
Section Check
Read the following question and justify who gets the
most accurate and precise value
Ronald, Kevin, and Paul perform an experiment to determine the value
of acceleration due to gravity on the Earth (980 cm/s2). The following
results were obtained: Ronald: 961 ± 12 cm/s2, Kevin: 953 ± 8 cm/s2,
and Paul: 942 ± 4 cm/s2.
A. Kevin got the most precise and accurate value.
B. Ronald’s value is the most accurate, while Kevin’s value is the
most precise.
C. Ronald’s value is the most accurate, while Paul’s value is the most
D. Paul’s value is the most accurate, while Ronald’s value is the most
Answer: C
Ronald’s answer is closest to 980 cm/s2,
hence his result is the most accurate.
Paul’s measurement is the most precise,
it’s within 4 cm/s2.
The precision of a measurement is one-half of the
smallest division of the instrument.
Formulate your OWN question
• Each person is to come up with a similar
question(s) and have the person in front or
behind you answer your question(s).
• In the measurement, 86.21, the “2” is (certain,
estimated) and (significant, not significant).
The “1” is (certain, estimated) and (significant,
not significant).