Download Significant Figures and Measurement Activity

Significant Figures and Measurement Activity
Objectives
Students traditionally have a very difficult time understanding which digits are significant,
especially zeros, in a number that represents something that has been measured. This activity
was designed so that students will explore and truly understand which digits are significant
when dealing with numbers that represent measured values.
Students will be able to:
1. use a measuring instrument to the limit of its precision.
2. determine which digit in a measured value is the most certain.
3. determine which digit in a measured value is the first uncertain value.
4. understand when zeroes are significant when determining the number of significant digits
in a measured number.
Materials
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1 blue paper ruler described below (per each pair of students)
1 red paper ruler described below (per each pair of students)
1 yellow paper ruler described below (per each pair of students)
several strips of green paper of different lengths (make sure some of them come out
to where zeroes will show up in the measurements)
Activity
1. Using a blue paper ruler with marks of 0 on one end and 10 on the other end, measure
several smaller pieces of green paper strips recording the results.
2. Using a red paper ruler the same length as the blue one up above but divided into 10 equal
spacings with only marks of 0,1,2,3,4,5,6,7,8,9, and 10 on it, measure the same green paper
strips you measured in activity 1 and record your results.
3. Using a yellow paper ruler the same length as the red one up above but with 10 additional
marks between each mark found on the red ruler, measure the same green paper strips you
measured in activity 1 above and record your results.
4. Have students analyze the results and discuss which digit in a measurement is the most
certain.
5. Have students analyze the results and discuss which digit in a measurement is the first
uncertain digit.
Conclusion Activity :
Discuss with students those measurements with zeroes in them to get students to understand
when those zeroes are significant and when they are not.
Many students have a very difficult time understanding significant digits and why they are
important in future calculations just by memorizing rules. Using carefully selected green
paper strips for students to measure, the students themselves can come up with the rules for
which digits are significant and their importance in future calculations. This activity can be
referred to when discussing significant figures in calculations.
Terms :
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significant/significance
certainty/uncertainty
Rules for deciding the number of significant figures in a measured quantity:
(1) All nonzero digits are significant:
1.234 g has 4 significant figures,
1.2 g has 2 significant figures.
(2) Zeroes between nonzero digits are significant:
1002 kg has 4 significant figures,
3.07 mL has 3 significant figures.
(3) Zeroes to the left of the first nonzero digits are not significant; such zeroes merely
indicate the position of the decimal point:
0.001 oC has only 1 significant figure,
0.012 g has 2 significant figures.
(4) Zeroes to the right of a decimal point in a number are significant:
0.023 mL has 2 significant figures,
0.200 g has 3 significant figures.
(5) When a number ends in zeroes that are not to the right of a decimal point, the zeroes are
not necessarily significant:
190 miles may be 2 or 3 significant figures,
50,600 calories may be 3, 4, or 5 significant figures.
The potential ambiguity in the last rule can be avoided by the use of standard exponential, or
"scientific," notation. For example, depending on whether 3, 4, or 5 significant figures is
correct, we could write 50,6000 calories as:
5.06 × 104 calories (3 significant figures)
5.060 × 104 calories (4 significant figures), or
5.0600 × 104 calories (5 significant figures).
What is an "exact number"?
Some numbers are exact because they are known with complete certainty.
Most exact numbers are integers: exactly 12 inches are in a foot, there might be exactly 23
students in a class. Exact numbers are often found as conversion factors or as counts of
objects.
Exact numbers can be considered to have an infinite number of significant figures. Thus,
number of apparent significant figures in any exact number can be ignored as a limiting
factor in determining the number of significant figures in the result of a calculation.