Math of Chem I Textbook Chapter 2 Aim: a) Determining the number of significant ... ·...

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= __________