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Significant Digits
Measurements
Description and Measurement
 Key Vocabulary
 Precision
 Accuracy
Description and Measurement
 Precision- how close
measurements are to
one another
 Example: If you
measure the width of a
floor tile several times
and you get: 1.0m,
1.1m, 1.0m, and 1.0m;
then your results are
precise
Description and Measurement
 Accuracy- comparison of a measurement
to an accepted value
 Example: when an archer shoots and arrow
and hits the bullseye, the archer is accurate
Description and Measurement
Description and Measurement
 Significant Figures- you can only be as precise
as your least precise measurement
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Digits other than zero (0) are always significant
Zeros after a decimal point are significant
Zeros between any other digit are significant
Initial zeros are not significant
Zeros at the end of a whole number may or may not
be significant
 Depends on if you place a decimal after the zero
Description and Measurements
 How many significant figures in these
examples
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0.00678 seconds
1234.098 meters
350 kilometers
5.00 milliliters
450. grams
Description and Measurements
 There are also rules to follow when
deciding the number of significant
digits in the answer to a calculation.
 It depends on the type of calculation
that you are doing.
Multiplying and Dividing with
Significant Digits
 The rule for multiplication and division is to
look at the total number of significant digits
in all of the numbers involved in the
calculation.
 Then, decide what is the smallest number
of significant figures you are working with
in the problem.
Example
 1.35/17=
 How many SD’s are in each number?
 1.35?
 17?
 1.35- 3 Significant Digits
 17- 2 Significant Digits
 2 is the smallest number of SD’s, so our
answer will have no more than 2
Significant Digits.
 0.0794117 rounded to 2 SD’s= 0.079
Adding and Subtracting with
Significant Digits
 The # of decimal places (not significant
digits) in the answer should be the same
as the least number of decimal places in
any of the numbers being added or
subtracted.
Example
5.67 J (two decimal places)
+
1.1 J (one decimal place)
+
0.9378 J (four decimal place)
7.7 J (one decimal place)
Quick Review
 Would the sum of 5.7 and 6.2 need to be
rounded? Why or why not?
 Would the sum of 3.28 and 4.1 need to be
rounded? Why or why not?
Quick Review
 Solve these problems using the correct
number of significant figures:
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43.25 + 213=
61.2-3.95=
64.992-3.9=
7.5+6.71=
180 / 42.512=
59.515 / 40=
6.757 x 35.6=
6.3 x 20 x 30=