Measuring Precision with Significant Digits
Precision is how finely tuned your measurements are or how close they can be to each other.
This depends on the measuring tool more than the operator. For example a meter stick, which
can measure to the .001 m (mm), is more precise than a car, which can measure to the 100 m
(hm). Precision is many times determined by the number of significant digits in the
measurement.
IDENTIFYING SIGNIFICANT DIGITS
Significant digits are those numbers that result from measurements (must have units). The
number of significant digits also called significant figures depends on the measuring instrument.
Prioritized rules used to determine significant digits (sd)
1. All non-zero digits are significant.
Examples:
Measurement
234 m
1,678 cm
.23 g
sd’s
3
4
2
Precision
to the m
to the cm
to the cg
3
4
6
to the mm
to the cm
to the m
2. All zeros between nonzero digits are significant.
Examples:
202 mm
1003 cm
.200105 m
3. Zeros to the right of a non-zero digit but to the left of an UNDERSTOOD or
INVISIBLE DECIMAL are NOT significant digits unless specified with a line over the
last significant zero.
Examples:
200 cm
1
to the m
109,000 m
1,000,000 mm
200 cm
200 cm
3
1
3
2
to the km
to the km
to the cm
to the dm
4. All zeros to the right of a decimal point but to the left of a non-zero digit are NOT
significant.
Examples:
0.0032 m
0.01294 g
0.00000002 L
2
4
1
to the 1/10th mm
to the 1/100th mg
to the 1/100th L
5. All zeros to the right of a decimal point and following a non-zero digit are significant.
Examples:
20.00 g
0.07080 mm
1.0400 cm
4
4
5
to the cg
to the 1/100th m
to the m
USING SIGNIFICANT DIGITS
Using significant digits can be considered a fancy method of rounding off numbers and
calculations so that your answers are scientifically and statistically accurate.
CONVERTING: Your converted answer must have the same number of significant digits as the
original measurement. Work the following examples.
.035 km = ____________ mm
750 mm = ______________ m 15.00 cm = _________ mm
15.00 cm = ____________ dam
20 km/h = _____________ mi/gal
CALCULATING: MULTIPLICATION OR DIVISION: Round your answer so it has the same
number of significant digits as the least precise measurement in your starting values:
d = 100 m t=11.28 s sp = d/t =
100 m/11.28 s =
d = 100 m t=11.28 s sp = d/t =
100 m/11.28 s =
CALCULATING: ADDITION OR SUBTRACTION: Round your answer so the number of
digits after the decimal point equals the fewest number of digits after the decimal point in your
starting values.
A5
Alternate Rule for Significant Digits
Here is an alternate rule for determining significant digits. The rule is really a "trick", which
might allow you to get the correct answers without really understanding the concepts. I
would recommend that students only use this as a secondary method, for the purpose of
checking their answers.
When you look at the number in question, you must determine if it has a decimal point or
not. If it has a decimal point, you should think of "P" for "Present". If the number does not
have a decimal point, you should think of "A" for "Absent".
Examples:
1. For the number 35.700, think "P", because the decimal point is present.
2. For the number 6500, you would think "A", because the decimal point is absent.
The letters "A" and "P" also correspond to the "Atlantic" and "Pacific" Oceans, respectively.
Now, assume the top of the page is north, and imagine an arrow being drawn toward the
number from the coast with the matching letter. Once the arrow hits a nonzero digit, it and all
of the digits after it are significant.
Example 1. How many significant digits are shown in the measurement 20 400 g? (Remember that we use spaces,
rather than commas, when writing numbers in science.
Well, there is no decimal, so we think of "A" for "Absent". This means that we imagine an arrow coming in from the
Atlantic Ocean, as shown below;
Absent decimal point
Pacific
Ocean
20 400 g
Atlantic
Ocean
The first nonzero digit that the arrow hits would be the 4, making the 4, and all digits to the left of the 4 significant.
Answer - There are three significant digits in the number 20 400 g
Here are the significant digits, shown in boldface: 20 400 g
Let's look at one more example.
Example 2. How many significant digits are shown in the number 0.090 m?
Well, there is a decimal, so we think of "P" for "Present". This means that we imagine an arrow coming in from the
Pacific ocean, as shown below;
Present decimal point
Pacific
Ocean
0.090 m
Atlantic
Ocean
The first nonzero digit that the arrow will pass is the 9, making it, and any digit to the right of it significant.
Answer - There are 2 significant digits in the number 0.090 m
Here are the significant digits, shown in boldface. 0.090 m
A6