Significant Digits/Figures

Sept. 2, 2014

SIGNIFICANT FIGURES OR DIGITS

• THE NUMBER OF SIGNIFICANT FIGURES INCLUDED IN A CALCULATION OR MEASUREMENT IS DEPENDENT ON THE ACCURACY OF THE MEASURING DEVICE OR INSTRUMENT USED TO MAKE THE ORIGINAL MEASUREMENTS

Exact v. Inexact Numbers

• Exact numbers – those numbers known exactly (by definition or by counting)

– One dozen = 12, one inch = 2.54 cm, 33 students in the room

• Inexact numbers – values with some uncertainty; anything measured using a piece of equipment (balance, graduated cylinder)

– Mass of penny = 3.03 grams

Precision v. Accuracy

• Precision – a measure of how closely individual measurements agree with one another (repeatability)– A balance is precise if it gives you the same

value for every trial

• Accuracy – how closely individual measurements agree with the correct or “true” value (bullseye)– a balance is considered more accurate with

increasing decimal places (+/- 0.0001 g is more accurate than +/- 0.01 g)

– Greater accuracy of an instrument means more significant figures.

SIGNIFICANT FIGURES

• RULE 1: Digits other than zero are always significant.

Examples:

96g 2 significant digits

61.4g 3 significant digits

0.52g 2 significant digits

SIGNIFICANT FIGURES

• RULE 2: One or more final zeros used after the decimal point are always significant (determined by the accuracy of the measuring device: i.e. - balance or electronic balance, etc.)

Example:

4.72 km 3 significant digits

4.7200 km 5 significant digits

82.0 m 3 significant digits

SIGNIFICANT FIGURES

• RULE 3: Zeros between two other significant digits are always significant.

Example:

5.029 m 4 significant digits

306 km 3 significant digits

6.02 x 10²³ particles 3 significant digits

SIGNIFICANT FIGURES

• RULE 4: Zeros used solely for spacing the decimal point are not significant. The zeros are place holders only.– You can tell a number is a placeholder if when you

remove the zeros, the number CHANGES its value

Example:

7000 g 1 significant digit

0.00783 kg 3 significant digits

SIGNIFICANT FIGURES

• RULE 5: Counting numbers and defined constants have and infinite number of significant digits

Summary

• SIGNIFICANT DIGITS: digits that represent actual measurements.

1. Digits other than zero.

2. Zeros after the decimal.

3. Zeros in the middle of significant

digits.

You Try!• How many sig figs in the following:

Examples:

a) 1001 km

b) 34.00 m

c) 129,870 m

d) .003 km

e) 1.003

f) .0072561 g

g) 20,000 cm

h) .0023 g

Number of Significant Figures:

a) 4

b) 4

c) 5

d) 1

e) 4

f) 5

g) 1

h) 2

CALCULATIONS WITH SIG FIGS• RULE: When multiplying or dividing

measurements, round off the final answer to the number of significant digits in your measurement having the least number of significant digitsExamples: 1. 2.03 cm x 36.00 cm = 73.08 cm²

= 73.1 cm²2. (1.13 m)(5.126122m) = 5.7925178 m²

= 5.79 m²3. 49.6000 cm² / 47.40 cm = 1.0464135 cm

= 1.046 cm

CALCULATIONS WITH SIG FIGS

• RULE: For addition and subtraction, the answer may contain only as many decimal places as the measurement with the least number of decimal places.

Examples:1) 677.1 cm 2) 34.231 g 3) 16.45 cm

39.24 cm 6.709 g - 8.329 cm + 6.232 cm + 18.20 g 8.121 cm722.572 cm 59.140 g = 8.12 cm

= 722.6 cm = 59.14 g

You Try!

• Addition

165.5 cm + 8 cm + 4.37 cm =

• Multiplication

2.6 cm x 3.78 cm =

You Try!

• Addition

165.5 cm + 8 cm + 4.37 cm = 177.87 cm

= 178 cm

• Multiplication

2.6 cm x 3.78 cm = 9.828 cm2

= 9.8 cm2