Download Significant Figures - Gulfport School District

MEASUREMENTS
What is the difference between these two
measurement rulers?
Should we record the same number for each
scale reading?
The second scale gives us more information, it is
more precise.
When writing measurements, we record the
digits that we are certain of plus one estimated
or uncertain digit. We consider these number
significant digits
8.9 cm
8.95 cm
6.00 cm
1120 cm
0.0260 cm
Significant Digits or Significant Figures
• We must be aware of the limits of precision
for each piece of lab equipment that we use.
• We must record our data to the proper
number of significant figures.
• You are always allowed one estimated figure
in measurements
• When measured quantities are given to you, it
is assumed that the proper number of
significant figures were recorded.
Rules for Counting Significant Figures
•
All non-zero digits are significant.
4
3
5
1 473 in _____
785 m _____
387.56 cm ____
• Zeros:
– Leading Zeros are not significant.
3
1
2
0.421 L _____
0.5 mL _____
0.0011 cm _____
– Captive Zeros are significant.
5
70 304 m _____
395.01 L _____
1.008 m _____
5
4
– Trailing Zeros are significant if there is a decimal point.
5
3
7
12.380 cm _____
1.30 in _____
1691.100 L _____
– Trailing Zeros are not significant if there is no decimal point.
2 500 in _____
800 m _____
9 010 mL _____
2
1
3
Determine the amount of significant
figures in the following examples:
3
967 L _____
4
0.111 0 mL _____
4
0.005 670 m _____
4
4.530 cm _____
4
2.700 mm _____
4
0.006 007 m _____
3
9.67 L _____
1
0.000 008 mL _____
6
0.800 008 m _____
Calculating with Significant Figures
• Multiply/Divide: The number with the
fewest number of sig figs will determine
the number of sig figs in the answer.
– Example
(13.92 g/cm3)(23.3 cm3 ) = 324.103 g
4 sig figs
3 sig figs
3 sig figs
324 g
Calculating with Significant Figures
• Addition/Subtraction: The number with
the fewest amount of decimal places
determines the amount of decimal places
in the answer .
– Example
3.76 g + 14.83 g + 2.1 g = 20.69 g
2 decimal
places
2 decimal
places
1 decimal
places
1 decimal
places
20.7 g
Rounding Rules
• Round this number to 3 sig. figs. 5.29753
• Count the number of significant figures you need from
left to right and underline the last sig. fig. you need.
• 5.28753
• Look at the number next to the number you
have underlined. Is it less than 5 or 5 and
up?
• 5.28753
• If the number is less than 5 (1-4) you will leave the
number you have underlined as it is.
• If the number is 5 or greater (5-9) you will round the
number underlined up to the next number.
• 5.29
Scientific Notation
• Scientific notation is the way that scientists
easily handle very large numbers or very small
numbers.
– Example: instead of writing 0.0000000056, we
write 5.6 x 10-9.
10000 = 1 x 104
24327 = 2.4327 x 104
1000 = 1 x 103
7354 = 7.354 x 103
100 = 1 x 102
482 = 4.82 x 102
10 = 1 x 101
89 = 8.9 x 101 (not usually done)
1 = 100
1/10 = 0.1 = 1 x 10-1
0.32 = 3.2 x 10-1 (not usually done)
1/100 = 0.01 = 1 x 10-2
0.053 = 5.3 x 10-2
1/1000 = 0.001 = 1 x 10-3
0.0078 = 7.8 x 10-3
1/10000 = 0.0001 = 1 x 10-4
0.00044 = 4.4 x 10-4
Scientific Notation
• The exponent of 10 is the number of places
the decimal point must be shifted to give the
number in long form.
– A positive exponent shows that the decimal point
is shifted that number of places to the right.
– A negative exponent shows that the decimal point
is shifted that number of places to the left.
– 46600000 = 4.66 x 107
– 0.00053 = 5.3 x 10-4