RULES AND PRACTICE

SIGNIFICANT FIGURES

WHY DO WE CARE ABOUT SIGNIFICANT FIGURES?

•Where are you?

HOW TO READ EQUIPMENT (NUMBER-LINE) FOR SIGNIFICANT FIGURES

1. Write down the numbers we are “sure of” meaning as exact as the lines and numbers on the equipment can go.

Example: The graduated cylinder shows that you have between 25ml and 26ml of liquid.

You write down 25.2. Go one number further. Look at the lines and spacing and guess. It is okay if you are a little off.

Example: It looks only slightly closer to the 25ml than the 26ml mark so you write down 25.4 ml

PRACTICE

• Do the practice problems on the board

ACCURACY, PRECISION, AND EXACTNESS

• Accuracy: how close a measurement is to “true” value.

• Precision - the repeatability of a measurement

• Exactness: making measurements to the correct level of uncertainty or significant figures

WHAT IS A SIGNIFICANT FIGURE

• It is the numbers in a measurement that can be counted on to be exact.

RULES FOR SIG. FIG.S

1. Non-zero numbers are always significant2. Any zeros between two significant numbers

are significant3. Any trailing zeros after the decimal point are

significant.

Exception: Exact numbers: If the statement is 100% true

and always true. All numbers count as SF.Examples: 12in = 1 ft 24 hrs = 1 day

PRACTICE

• How many significant figures are in each number

1.35002.5013.0.0204.8000005.50000001

PRACTICE

• How many significant figures are in each number

1.0.00005002.8.260 x 102

3.9000.014.5010005.900000000.0

ROUNDING TO A CERTAIN NUMBER OF SIGNIFICANT FIGURES

• Sometimes when doing a math problem you get a calculator answer with more numbers than you have significant figures. In that case you need to round.

• For example:Round 436.76 to 4 significant figures

(so you want to keep the first 3 sig figs and round the 4th whichever direction is correct. #1-4 keep the same #,

#5-9 round up)

At the end check by counting the # of Sig Figs and checking the digits are in the right places.

ROUNDING PRACTICE

1. Round 1235 to 2 significant figures2. Round 0.530601 to 3 significant figures3. Round 5302146655 to 4 significant

figures4. Round 0.000002500 to 1 significant

figure5. Round 6.00021 to 3 significant figures

CLASS/HOME WORK

• Read chapter 2.5• Answer Questions and Problems (located at the

end of the chapter, pg 47): #37-39, 43

ADDING AND SUBTRACTING SIGNIFICANT FIGURES

Steps:1.Change all measurements to the same unit/exponent before adding or subtracting.2.Put the numbers in the calculator and get the answer.3.Round the answer to the decimal place of the original number with least exact place (tenths, hundredths, etc.)

ADDING/SUBTRACTING PRACTICE

1. 1 + 1.52. 55 + 9.4323. 432 – 204. 0.0043 + 0.0115. 4008 - 550

ADDING/SUBTRACTING PRACTICE

1. 543.234 + 7652.21 + 32.42. 88000 – 5377 - 63300.03. 0.002345 + 0.0424 – 0.00100004. 500000.0 + 328 – 0.99325. 7.345 + 432.0 – 30

CLASS/HOME WORK

• If you need help, we are still in chapter 2.5• Answer: #46, 49-51, 52abc

• Note: 52d is harder than I expect you to be able to do at this point. Give it a try if you want.

RULES FOR MULTIPLYING AND DIVIDING

1. Put it in the calculator and get the answer.2. Count the number of significant figures for the

original numbers.3. Round the answer’s significant figures to the

same amount as the original number with the least significant figures.

PRACTICE

1. 23 x 0.0432. 3.05 / 0.000452103. 0.00020402 x 8000004. 320 / 0.004210 x 0.00935. 45300001 x 0.0004320 / 0.00235

RULES FOR MULTIPLYING / DIVIDING WITH EXPONENTS (SCIENTIFIC NOTATION)

1. Multiply/divide any numbers in front of the 10x.

2. When multiplying exponents, add them together

3. When dividing exponents subtract.4. Write answer with correct significant

figures.

PRACTICE

1. 1 x 103 x 4 x 104

2. 0.045 x 10-6 / 5.01 x 106

3. 5030 x 1035 x 3.4 x 10-27 / 0.4 x 104

HOMEWORK

Chapter 2: 47, 48, 53, 54 (with answers)