SIGNIFICANT FIGURES
RULES AND PRACTICE
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 significant
2. Any zeros between two significant numbers
are significant
3. 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.
2.
3.
4.
5.
3500
501
0.020
800000
50000001
PRACTICE
• How many significant figures are in each number
1.
2.
3.
4.
5.
0.0000500
8.260 x 102
9000.01
501000
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.
2.
3.
4.
5.
Round 1235 to 2 significant figures
Round 0.530601 to 3 significant figures
Round 5302146655 to 4 significant figures
Round 0.000002500 to 1 significant figure
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.
2.
3.
4.
5.
1 + 1.5
55 + 9.432
432 – 20
0.0043 + 0.011
4008 - 550
ADDING/SUBTRACTING PRACTICE
1.
2.
3.
4.
5.
543.234 + 7652.21 + 32.4
88000 – 5377 - 63300.0
0.002345 + 0.0424 – 0.0010000
500000.0 + 328 – 0.9932
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.
2.
3.
4.
5.
23 x 0.043
3.05 / 0.00045210
0.00020402 x 800000
320 / 0.004210 x 0.0093
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)