1. Significant (Measured) Digits
Measuring with Precision

2. Significant Digits (sd)
Defn: Those numbers that result from directly measuring an object. It shows the precision of the measurement.
Units must be included (no units no sd)
The precision of the measurement depends upon the measuring instrument
Use the following PRIORITIZED list to determine the number of sd’s in a measurement, calculation, or conversion

3. Rule 1: All nonzero digits are significant (they were measured)
Samples
a m
b cm
c g
SD’s and precision
a. 3 sd to the m
b. 4 sd to the cm
c. 2 sd to the cg

4. Samples a. 202 mm b. 1003 cm c. 0.200105 m SDs and precision
Rule 2: All zeros between nonzero (or significant) digits are significant
Translation: In between 0s must be measured
Samples
a. 202 mm
b cm
c m
SDs and precision
a. 3 sd to the mm
b. 4 sd to the cm
c. 6 sd to the mm

5. a. 1 sd to the m b. 3 sd to the km b. 109,000 m c. 1 sd to the km
Rule 3: Zeros to the right of a nonzero digit but to the left of an understood decimal are NOT significant unless otherwise indicated.
Translation: 0s at the end of a whole number are NOT measured unless marked.
a. 1 sd to the m
b. 3 sd to the km
c. 1 sd to the km
d. 3 sd to the cm
e. 2 sd to the dm
a cm
b. 109,000 m
c. 1,000,000 mm
d. 200 cm
e. 200 cm
(a bar over a zero indicates the last measured zero)

6. Samples a. 0.0032 m b. 0.01294 g c. 0.00000002 L SDs and precision
Rule 4: All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant.
Translation: 0s in front of a number less than 1 are NOT measured.
Samples
a m
b g
c L
SDs and precision
a. 2 sd to the .1 mm
b. 4 sd to the .01 mg
c. 1 sd to the .01 mL

7. Rule 5: All zeros to the right of a decimal point and following a nonzero digit are significant
Translation: 0s at the end of a decimal number are measured.
Samples
a g
b mm
c cm d
SD’s and precision
a. 4 sd to the cg
b. 4 sd to the .01 mm
c. 5 sd to the mm
d. 0 sd

8. How to use this information when converting/evaluating measures
Examine the number & go through rules IN ORDER
Rule 1 - underline any nonzero digits
Rule 2 - underline any zeros between these
Rule 3 - place an ‘n’ under the zeros at the end of a whole number (after any overlined 0s)
Rule 4 - place an ‘n’ under zeros in front of a number less than one
Rule 5 - underline zeros at the end of a decimal number
Count the number of underlined digits = # sd

9. When converting measurements
Rule: The converted measurement must have exactly the same precision as the original measurement.
Ex. When converting 6.0 cg to dag is the conversion .006 dag or dag?
6.0 cg has 2 sd so the conversion must have 2 sd. Which conversion has 2 sd?
Answer: dag

10. How to use SD rules when multiplying/dividing
Rule: Your calculation (answer) must have the same precision as the LEAST precise original measurement
Find the number of significant digits in each of the starting numbers and note the lowest number of significant digits
ex cm x 3 cm (lowest # of sd is 1)
Calculate your answer
Round the answer to the lowest # of sd found step 1
2.40 cm x 3 cm = (7.2 cm2) = 7 cm2