1. Significant Figures and Rounding

2. Significant Figures
Significant figures - show accuracy in measurements & calculations
Significant figures in a measurement consist of all of the digits known with certainty plus one digit that is an estimate.
The number of significant figures in a measurement indicates to precision in the measurement it is.
A balance that reads to the 1.0 gram is less certain in a measurement that a balance that reads to grams.

3. Rules for Identifying sig. figs. In a Measurement
The digits 1 through 9 ( all non-zero digits) are ALWAYS significant.
243 Has 3 significant figures
Four significant figures
How many significant figures are in
5 Significant digits
How many significant figures are in 3.1
2 significant digits

4. Rules for Identifying sig. figs. In a Measurement
Middle zeros are ALWAYS significant figures (zeros between non-zero digits)
207 Three significant figures
Five significant figures
How many significant figures are in 207.5
4 significant digits
How many significant figures are in 60,007
5 significant digits

5. Rules for Identifying sig. figs. In a Measurement
Leading zeros are NEVER significant. Leading zeros are zeros that occur at the beginning of a number. Leading zeros function to indicate the position of the decimal point.
Two significant figures
Five significant figures
How many significant figures are in
3 significant digits
How many significant figures are in
5 significant digits

6. Rules for Identifying sig. figs. In a Measurement
Ending zeros are zeros at the end of the number. They are SOMETIMES significant. They ARE significant if there is a decimal point anywhere in the number. If no decimal point, ending zeros are NOT significant.
Four significant figures
Four significant figures
200 One significant figure
How many significant figures are in 62.00
4 significant digits
How many significant figures are in 24.70
How many significant figures are in 360,000
2 significant digits

7. The do not affect the number of sig figs in your final answer
Counting, exact and defined numbers have an infinite number of significant figures.
Pi-
………
Avogadro’s number-
x 10^23
A bakers dozen
The do not affect the number of sig figs in your final answer

8. EXERCISE 1 10423 10423 5 sig figs 1230.0 1230.0 5 sig figs 150
0.0032
sig figs
3300
sig figs
10.0
sig figs
sig figs

9. Rounding
Rounding is the process of deleting extra digits from a calculated number. 1. If the first digit to be dropped is less than 5, that digit and all the digits that follow it are simply dropped rounded to three significant figures becomes If the first digit to be dropped is greater than or equal to 5, the excess digits are all dropped and the last significant figure is rounded up rounded to three significant figures becomes 62.9

10. Round The following 423.78 to three significant figures 424
B to two significant figures
C to four significant figures
22.55
D to three significant figures
(must have decimal)
E to one significant figure
0.4
F to three significant figures
7.21

11. Calculations Using Significant Figures
A calculated number cannot be more precise than the data numbers used to calculate it. In other words: the answer can’t be more precise than any of the original numbers in the problem.

12. Addition and Subtraction
*Two different rules apply: The Rule for Addition & Subtraction is DIFFERENT than the Rule for Multiplication and Division
1. Addition & Subtraction
In addition and subtraction, the last digit in the answer must be expressed to the same decimal place value as the entry with the ____least________ accurate decimal position.
(accurate to the hundredths position)
(accurate to the hundred thousandths position)
37.916__ (accurate to the thousandths position)
Becomes to the hundredths position
(accurate to the tenths position)
(accurate to the thousandths position)
Becomes 74.8 to the tenths position l

13. Addition and Subtraction
*Write the given calculated answer in the correct number of significant figures. Look at decimal places only
  a =
3.72
= 71.68
71.7
3.289 – 0.66 = 2.629
2.63
5.976 – = 5.497
no change =
no decimal place in first number
– =
7.9

14. Multiplication and Division
In multiplication and division the number of significant figures in the product or quotient must be the same as in the number in the calculation that contains the least significant figures
This is the rule we mainly use!!!

15. 6.038 x 2.57 =
Correct answer is 15.5 because the three significant digits in limits our answers to three significant digits
120.0 ÷ = 30
Correct answer is because each entry has four significant digits so your answer must have four significant digits.
(3.130 x 3.14) ÷ 3.1 =
Correct answer is 3.2 because the least number of significant digits in the entries is two so our answer must only have two significant digits.

16. Multiplication and Division Practice
Count total number of Sig Figs!!!! .
3.751 x 0.42 =
1.6
x =
0.014
3.27 / 4.6 =
0.71
49.7 / =
832
(7.2 x 0.69) / 3.24 =
0.87
269 / (3.270 x 4.6) = 18