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Aim:a) Determining the number of significant
figures in a value.b)To round the solutions of calculations
using significant figures.
Math of Chem ITextbook Chapter 2
Significant Figures
Significant figures represent the accuracy
and precision of a measurement
The more significant figures in a number,
the more precise the measurement.
Significant figures: All known (certain) values read from an instrument plus one estimated value.
Precision vs. Accuracy
Precision- how close repeated measured values are to each
other.
Accuracy- how close a measured value is to the accepted
value.
Precision vs. Accuracy
Precision also refers to the number of KNOWN digits in a
value.
Determining Significant Figures
Rules:
All non-zero digits are significant.
Ex: 5
All zero’s sandwiched between non-zero digits are significant. Ex: 5005
All zero’s lagging after a non-zero digit when a demical is present are significant.
Ex: 0.00500
5.0000Instrument precision
Non Significant Figures Leading zeroes are NEVER significant.
Ex: 0.0001
Zeroes lagging after a nonzero digit with no decimal are NEVER significant.
Ex: 5000
>
How many significant figures are present in the following numbers?
4000______ 600100______
2.00 ________ 0.00052 _______
0.00400 ______ 600.0 _____
Determine the number of significant figures
in each of the following numbers
1) 0.001 9) 1.001
2) 3.00 10) 2000
3) 520.1 11) 0.010
4) 0.040000 12) 15,000
5) 520 13) 174.0
6) 300
7) 4001
8) 500, 100
Practice
1) 1.001
2) 2000
3) 0.010
4) 15,000
5) 174.0
Math with Sig Figs
When performing calculations in Chemistry
you must round your answer to be as precise
as the LEAST precise measurement value.
This type of rounding takes significant figures
into account in order to maintain precision.
Multiplication/Division
When multiplying or dividing:
◦ Round the answer to have the same
number of significant figures as the value
with the least number of significant figures.
ex. 2.050 x 4.1 = ex. 21,400/5.20 =
Examples
1. 7.60 g x 3.0 g = ____________
2. 11.05 cm x 2.55 cm = ____________
3. 12 L x 6.3 s = ____________
4. 9.450 g2 / 3.0 g=____________
5. 200.0 g / 5.0 cm3 = ____________
6. 6300 kg / 1.7 s = _____________
Addition/Subtraction Rules
When adding or subtracting:
◦ Round the answer to have same number of
digits after the decimal as the number with
the fewest.
ex. 2.48 L + 5.937 L = ex. 6.550 km – 4.2129 km =
Examples
1. 5.600 g + 3.40 g = ____________
2. 7.894 s + 0.1 s= ____________
3. 10.0 mL+ 14.044 mL= ____________
4. 5.80 cg – 3.4 cg= ____________
5. 15.0043 K – 10.09 K = ____________
Mixed
1. (7.60 g x 3.0 g) + 7.5 g2 = __________
2. (12.7 km + 8.90 km) – (11.05 km x 2.55 km) =
______________
3. (12 mm3 / 6.3 mm) – (6.7 mm x 4.0 mm) = ____
4. (9.450 g + 7.80 g) / 3.0 cm3=__________
5. (205.6 ms + 18 ms) x 5.67 ms= __________