1. Math of Chem I
Textbook Chapter 1
Aim:
a) Determining the number of significant figures in a value.
b)To round the solutions of calculations using significant figures.

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.

3. Precision vs. Accuracy
Precision- how close repeated measured values are to each other.
Accuracy- how close a measured value is to the accepted value.

4. Precision vs. Accuracy
Precision also refers to the number of KNOWN digits in a value.

5. 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:
5.0000
Instrument precision

6. Non Significant Figures
Leading zeroes are NEVER significant.
Ex:
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______ ______
2.00 ________ _______
______ _____

7. Determine the number of significant figures in each of the following numbers
) 1.001
) 2000
) 0.010
) 15,000
) 174.0
300
4001
500, 100

8. Practice
1.001
2000
0.010
15,000
174.0

9. 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.

10. 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 x 4.1 = ex. 21,400/5.20 =

11. Examples 7.60 g x 3.0 g = ____________
11.05 cm x 2.55 cm = ____________
12 L x 6.3 s = ____________
9.450 g2 / 3.0 g=____________
200.0 g / 5.0 cm3 = ____________
6300 kg / 1.7 s = _____________

12. 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 L L = ex km – km =

13. Examples 5.600 g + 3.40 g = ____________ 7.894 s + 0.1 s= ____________
10.0 mL mL= ____________
5.80 cg – 3.4 cg= ____________
K – K = ____________

14. Mixed (7.60 g x 3.0 g) + 7.5 g2 = __________
(12.7 km km) – (11.05 km x 2.55 km) = ______________
(12 mm3 / 6.3 mm) – (6.7 mm x 4.0 mm) = ____
(9.450 g g) / 3.0 cm3=__________
(205.6 ms + 18 ms) x 5.67 ms= __________