Significant Digits
- -all measurements involve uncertainty.
- -the certainty of any measurement is communicated by the number of significant digits in the measurement
- -significant digits include the digits you are certain about, and a final, uncertain digit you estimate
- -the digits you record from a measurement are termed significant digits
Rules for determining significant digits
1. All non-zero numbers are significant
- - 7.886 has 4 significant digits
- - 19.4 has 3 significant digits
- - 527.266 992 has 9 significant digits
2. All zeros that are located between two non-zero numbers are significant.
- 408 has 3 significant digits
- 25 076 has 5 significant digits
3. Zeros that are located to the left of a measurement are not significant
-
0.0907 has 3 significant digits
4. Zeros to the right of a measurement may or may not be significant.
-
22 700 may have 3 significant digits if the measurement is approximate
-
22 700 may have 5 significant digits if the measurement is exact
Rules for reporting significant digits in calculations
1. Multiplying and dividing:
The value with the fewest number of significant digits, going into the calculation,
determines the number of significant digits in your answer.
77.8 km/h x 5.9015 h = 459.136 7 km = 459 km the answer must have 3
significant digits to express the same certainty as the value, 77.8 km/h,
with the fewest significant digits in the question.
2. Adding and subtracting:
The value with the fewest number of decimal places, going into the calculation,
determines the number of decimal places that you should report in your answer.
12.5 g + 145.67 g + 70.5456 g + 3.001 g = 231.7166 g = 231.7 g
3. Rounding Off
To get the appropriate number of significant digits for answers from calculations you do, it is necessary to round off your answers.
- If your answer ends in a number that is greater than 5 increase the preceding digit by 1.
2.346 rounded to 3 significant digits is 2.35
- If your answer ends in a number that is less than 5 leave the preceding number unchanged.
2.343 rounded to 3 significant digits is 2.34
- If your answer ends with 5, increase the preceding number by 1 if it is odd, leave the preceding
number unchanged if it is even.
18.35 rounded to 3 significant digits is 18.4
18.25 rounded to 3 significant digits is 18.2
Exercises:
1. Determine the number of significant digits in the following measurements.
a) 32.07 m
b) 0.0047 g
c) 5 x 105 kg
d) 6400 s
e) 204.0 cm
f) 0.000 001 µm
g) 0.156 345 g
h) 10.0 cm
2. Express each answer using the correct number of significant digits.
a) 55.671g + 45.78
b) 1.9 mm + 0.62 mm
c) 87.9478 L – 86.25L
d) 0.350 mL + 1.70 mL + 1.019 mL
e) 5.841 g x 6.03 g
f) 17.51g ÷ 2.2 cm3
g) 23 457.12 cm x 45.341 cm
