1. Significant Figures

2. Precision: How well a group of measurements made of the same object, under the same conditions, actually agree with one another.
These points are precise with one another but not “accurate”.

3. Accuracy: represents the closeness of a measurement to the true value.
Ex: the bulls-eye would be the true value, so these points are accurate.

4. Why Significant Figures?
Precision is determined by the instrument we use to take measurements. So, our calculations must be only as precise as the measurements.
NOTE: The last digit of any measurement is always a “guess” therefore it is uncertain.

5. Measuring: precision

6. Other instruments…

7. Rounding
You will need to round off sig. figs when you multiply, divide, add or subtract.
When rounding off to a certain place value, you need to look one place farther.
If the next digit is a 5 or higher, you round the digit before it UP.
If the next digit is a 4 or lower, you DON”T round up.

8. Using sig figs: The Rules!
Digits from 1-9 are always significant.
Zeros between two other significant digits are always significant
Zeros at the beginning of a number are never significant.
Zeros at the end of a number are only significant IF there is a decimal place.

9. Example:
Number of sig figs
Why?
453kg 3
All non-zero digits are always significant.
5057L 4
Zeros between 2 sig. dig. are significant.
5.00
Additional zeros to the right of decimal and a sig. dig. are significant.
0.007 1
Placeholders are not sig.

10. Problems: Indicate the number of significant figures...
______
______
______
______
______
______
______
______
______
______

11. ___4___
___3___
___3___
___3___
___3___
___2___
___2___
___4___
___7___
___6___

12. Round these numbers to 3 significant figures
= ___________
8008= _____________
24.567= _________
100.04= __________
= ____________
1.675 x 103= ____________

13. = __5.87_________
8008= ___8010__________
24.567= __24.6_______
100.04= ___100._______
= __5630__________
1.675 x 103= ___1.68 x 103 _____

14. Multiplying and Dividing
RULE: your answer may only show as many significant figures as the multiplied or divided measurement showing the least number of significant digits.
Example: cm x 3.10 cm = 69.3
(only 3 sig figs allowed)

15. Multiplying and Dividing Practice
x ______
x 0.23 ______
÷ ______
÷ 4.1 ______
x ______
x ______
÷ ______
x 23 ______
÷ ______
x 12 ÷ 12.5 ______

16. x __110.____
x 0.23 __7.6____
÷ __38.1____
÷ 4.1 __5.7____
x __26____
x __0.9____
÷ __2100____
x 23 __2000____
÷ __1000____
x 12 ÷ 12.5 __110____

17. Adding and Subtracting:
RULE: your answer can only show as many place values as the measurement having the fewest number of decimal places.
Example:
3.76 g g g = 20.7 g
3.76 is precise to the hundredths place, is precise to the hundredths place, 2.1 is only precise to the tenths place, so we round off the final answer to the tenths place.

18. Adding and Subtracting Practice
______
______
______
______
______
______
______
______
______
______

19. __2.65____ __2.61____ __280____ __1.03____ __4.22____ __1.1____ __383____ __233____ __239____ __122.2____

20. Scientific Notation

21. Scientific Notation
Scientists have developed a shorter method to express very large numbers.
Scientific Notation is based on powers of the base number 10.

22. 123,000,000,000 in s.n. is 1.23 x 1011
The first number 1.23 is called the coefficient. It must be between
The second number is called the base . The base number 10 is always written in exponent form. In the number 1.23 x 1011 the number 11 is referred to as the exponent or power of ten.

23. To write a small number in s.n. ex: 0.00064
First move the decimal after the first real number and drop the zeroes. Ex: 6.4
Next, count the number of places moved from the original decimal spot to the new decimal spot. Ex: 4
Numbers less than 1 will have a negative exponent. Ex: -4
Finally, put it together. Ex: 6.4 x 10-4

24. Scientific Notation Practice
_______________
_______________
_______________
_______________
_______________
1.23 x 10-4 _______________
7.51 x _______________
3.09 x 10-3 _______________
2.91 x 102 _______________
9.6 x 104 _______________

25. __8.26 x 10-2___
__2.63 x 106___
__9.45 x 105___
__1.76 x 106___
__5.07 x 10-3___
1.23 x 10-4 __ _____
7.51 x __751000______
3.09 x 10-3 __ _____
2.91 x 102 __291_________
9.6 x 104 __96000_______