1. Significant Digits and Scientific Notation

2. Accuracy vs Precision
An accurate measurement is close to the true value.
Precision gives an idea of the reliability of a measurement
Precision is a measure of the agreement among a series of measurements.

4. Significant Digits
Significant digits are the digits in a measurement that are known to be precise

5. Which digits are significant?
Not Significant
Non-zero digits
Zeros in the middle
Zeros at the end
As long as there is a decimal point somewhere in the number
Exact numbers and integers have infinite significant figures
Leading zeros
“ x10n ” in scientific notation

6. 1000
1000.
01000
1 x 103
1.0 x 103
87032
74000
8.900

7. Sig. Figs. in Lab
All of the digits in the readout a digital apparatus are significant and should be written down.
Don't round off or drop zeros.
Your calculator is not included.

8. Analog Scales
The digit not read from the written scale is the estimated digit
Example: 82.5mL estimated digit = 5
Analog scales are read to one tenth of the smallest graduation present.
Example: Scale is graduated every 1 mL, so reading should be to the nearest 0.1 mL.
Don't round off or drop zeros.
Example: 29.0mL

10. Great Measuring

11. Good Measuring

12. Needs Work

13. Scientific Notation
Use scientific notation to eliminate place holding zeros.
Move the decimal so that only 1 digit remains in front of the decimal. Then change the exponent accordingly.
If you move the decimal to the right the exponent is negative.
If you move the decimal to the left the exponent is positive
Round to the correct number of sig figs

14. When taking a number out of scientific notation move the decimal in the opposite direction and fill the empty spaces with 0’s
If the exponent is negative move the decimal point to the left
If the exponent is positive move the decimal point to the right
3.46 x 10-5
8.138 x 108

15. Sig Figs part ii

16. Calculations with Sig. Figs.
Calculations involving measurements
Significant figures depends on the sig figs of the measurements
The weakest link principle
Least number of sig figs is limiting
One rule for addition and subtraction different rule for multiplication and division.

17. Addition and Subtraction
RULE: When adding and subtracting, the result should have the same number of decimal places as the least precise number added.
Example: = =

18. Multiplication and Division
RULE: When multiplying or dividing, the result should have the same number of significant figures as the number with least significant figures.
Example: 3.28 x 2.1
÷ 7.20

19. Longer Calculations
In a calculation with several steps, the final result must be rounded off to the correct sig. figs.
Rounding off intermediate results may cause cumulative round-off errors.
Don’t round until the end.
(2.34 x 1.3) =
8.35 – (5.31 ÷ 3.001)=