Significant Figures
1. Explain what significant figures are.2. Use Significant figures in measurements and calculations.3. Understand how significant figures impact precision.
Why do we need to know significant figures?We as scientists need to measure
things as we perform experiments.Instruments have different degrees of
precisionWe measure to the last known
calibration, and estimate the unknown.
Measurements in ExperimentsChapter 1
Significant Figures
Even though this ruler is marked in only centimeters and half-centimeters, if you estimate, you can use it to report measurements to a precision of a millimeter.
The Rules
Significant Figures – The Rules1. Nonzero numbers 1 – 9 are
always significant.
Examples: 1 meter 1 sig fig 92 liters 2 sig figs 34578 grams 5 sig figs
Significant Figures – The Rules2. Imbedded zeros (zeros between
nonzero numbers) are always significant.
Examples: 202 cm 3 sig figs10509 mL 5 sig figs2039 kg 4 sig figs90009 g 5 sig figs
Significant Figures – The Rules3. Leading zeros are never significant.4. Trailing zeros after a nonzero
number after the decimal are significant.
Examples:0.00000540 g 3 sig figs0.3700 mm 4 sig figs0.00101 L 3 sig figs
Significant Figures – The Rules5. Trailing zeros before the decimal
are significant only if the decimal point is specified.
Examples:100. dg 3 sig figs100 dg 1 sig fig8900 km 2 sig figs8900. km 4 sig figs
Exact NumbersAn exact number is a number that cannot
be changed. (Cannot be halved or split up)Ex. 2 atoms, 1 proton, a hundred dollar bill
We include most conversion factors as exact numbers Ex. 1m = 100 cm
When you work with exact numbers, you consider them to have infinite sig figs.
(You don’t have to worry about them!)
RECAP #1
Leading Zeros Imbedded Zero
0.00770800
Nonzero numbers Trailing Zeros
after the decimal
6 significant figures
RECAP #2
Leading Zeros Imbedded Zero
(none)
22060 Nonzero numbers
Trailing zero with no decimal
4 significant figures
Lets Practice!
56 meters
2 sig figs
Rule 1
20 grams
1 sig figRule 1, 5
303.0 mL
4 sig figsRule 1, 2,
4
200 kilograms
1 sig figRule 1, 5
207 kilometers
3 sig figsRule 1,2
0.7900 grams
4 sig figsRule 1,3,4
0.0096070 m
5 sig figsRule 1,2,3,4
102000 km
3 sig figsRule 1,2,5
1.10 x 102
hm
3 sig figs Rule 1, 4
2.2 x 1034 atoms
infinite sig figs
Rounding NumbersIf you have to round and the
number you are looking to round is less than 5, don’t round.Example:
214round to 2 s.f.Answer = 210
Rounding NumbersIf you have to round and the
number you are looking to round is 5 or greater, round up.Example:
215round to 2 s.f.Answer = 220
Adding and subtracting with significant figures.When adding or subtracting
significant figures, you round your answer to the least number of places after the decimal that are contained in your problem.
YOU ARE LOOKING AT PLACES AFTER
THE DECIMAL NOT SIGNIFICANT
FIGURES!
Example:2.00 + 4.0 = 6.0
You look for the least number of PLACES after the decimal.
2.00 = 2 places after the decimal4.0 = 1 place after the decimalYour answer can only have one place after the
decimal.
Example:
2.0 + 4 = 6
2.0 = 1 place after the decimal4 = no places after the decimalYour answer can not have any places
after the decimal.
Example:0.05560 – 0.001 = 0.0546
=0.055
0.05560 = 5 places after the decimal0.001 = 3 places after the decimalYour answer can only have 3 places
after the decimal.
Let’s Practice
17.0 – 0.4753 = 16.5247
Answer16.5
37.00 + 0.4753 + 19 =56.4753
Answer56
100.0 – 71.52 = 28.48
Answer28.5
0.075 + 11 + 9.2 = 20.275
Answer20
Multiplying and Dividing with Significant FiguresWhen multiplying or dividing with
significant figures, your answer must be rounded to the least number of significant figures in the problem.
YOU ARE LOOKING AT SIGNIFICANT FIGURES NOT
PLACES AFTER THE DECIMAL!
Example20.0 x 14.22 =
284.4
Answer284
430 x 0.003 = 1.29
Answer1
2020 x 790.00 = 1600000
Answer1.60 x 106
50.0 / 0.020 = 2500
Answer2500
50.0 / 0.02000 = 2500
Answer2.50 x 103