1. Significant Figures

2. What is a significant figure?
There are 2 kinds of numbers:
Exact: the amount of money in your account. Known with certainty.

3. What is a significant figure?
Approximate: weight, height—anything MEASURED. No measurement is perfect.

4. When to use Significant figures
When a measurement is recorded only those digits that are dependable are written down.

5. When to use Significant figures
If you measured the width of a paper with your ruler you might record 21.7cm.
To a mathematician , or is the same.

6. But, to a scientist 21.7cm and 21.70cm is NOT the same
21.700cm to a scientist means the measurement is accurate to within one thousandth of a cm.

7. How do I know how many Sig Figs?
Rule: Any non-zero numbers will ALWAYS be significant.

8. How do I know how many Sig Figs?
Rule: In whole numbers that end in zero, the zeros at the end are not significant.

9. How many sig figs? 7 40
0.5
7 x 105
7,000,000 1

10. How do I know how many Sig Figs?
Rule: If zeros are sandwiched between non-zero numbers, the zeros become significant.

11. How do I know how many Sig Figs?
Rule: If zeros are at the end of a number that has a decimal, the zeros are significant. These are called trailing zeroes.
If zeroes are at the beginning of a number (numbers less than 1), the zeroes are said to be insignificant. These are called leading zeroes.

12. How many sig figs here?
1.2
204
56.76
4.00
0.0792
7,083,000,000 2 3 4

13. How many sig figs here?
3401
2100
2100.0
5.00
8,000,050,000 4 2 5 3 6

14. What about calculations with sig figs?
Rule: When adding or subtracting measured numbers, the answer can have no more places after the decimal than the LEAST of the measured numbers.

15. Add/Subtract examples
2.45cm + 1.2cm = 3.65cm,
Round off to = 3.7cm
7.432cm + 2cm = 9.432

16. Multiplication and Division
Rule: When multiplying or dividing, the result can have no more significant figures than the least reliable measurement.

17. A couple of examples Round to 730 75.8cm x 9.6 cm = 727.68 cm2