Transcript Significant Figures

Significant Figures
SPH3U
• 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”.
• 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.
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.
Measuring: precision
Other instruments…
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.
Using sig figs: The Rules!
1. Digits from 1-9 are always significant.
2. Zeros between two other significant
digits are always significant
3. Zeros at the beginning of a number are
never significant.
4. Zeros at the end of a number are only
significant IF there is a decimal place.
Example:
453kg
Number of
sig figs
3
5057L
4
5.00
3
0.007
1
Why?
All non-zero digits are
always significant.
Zeros between 2 sig.
dig. are significant.
Additional zeros to the
right of decimal and a
sig. dig. are significant.
Placeholders are not sig.
Problems: Indicate the number
of significant figures...
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.235
2.90
0.0987
0.450
5.00
2300
230
230.0
9870345
1.00000
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
1.235
2.90
0.0987
0.450
5.00
2300
230
230.0
9870345
1.00000
___4___
___3___
___3___
___3___
___3___
___2___
___2___
___4___
___7___
___6___
Round these numbers to
3 significant figures
1)
2)
3)
4)
5)
6)
5.8746 = ___________
8008= _____________
24.567= _________
100.04= __________
5634.3999= ____________
1.675 x 103= ____________
1)
2)
3)
4)
5)
6)
5.8746 = __5.87_________
8008= ___8010__________
24.567= __24.6_______
100.04= ___100._______
5634.3999= __5630__________
1.675 x 103= ___1.68 x 103 _____
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: 22.37 cm x 3.10 cm = 69.3
(only 3 sig figs allowed)
Multiplying and Dividing Practice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
42.3 x 2.61
32.99 x 0.23
46.1 ÷ 1.21
23.3 ÷ 4.1
0.61 x 42.1
47.2 x 0.02
47.2 ÷ 0.023
100 x 23
124 ÷ 0.12
120 x 12 ÷ 12.5
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
42.3 x 2.61
32.99 x 0.23
46.1 ÷ 1.21
23.3 ÷ 4.1
0.61 x 42.1
47.2 x 0.02
47.2 ÷ 0.023
100 x 23
124 ÷ 0.12
120 x 12 ÷ 12.5
__110.____
__7.6____
__38.1____
__5.7____
__26____
__0.9____
__2100____
__2000____
__1000____
__110____
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 + 14.83 g + 2.1 g = 20.7 g
3.76 is precise to the hundredths place, 14.83 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.
Adding and Subtracting Practice
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2.634 + 0.02
2.634 - 0.02
230 + 50.0
0.034 + 1.00
4.56 - 0.34
3.09 - 2.0
349 + 34.09
234 - 0.98
238 + 0.98
123.98 + 0.54 - 2.3
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2.634 + 0.02
2.634 - 0.02
230 + 50.0
0.034 + 1.00
4.56 - 0.34
3.09 - 2.0
349 + 34.09
234 - 0.98
238 + 0.98
123.98 + 0.54 - 2.3
__2.65____
__2.61____
__280____
__1.03____
__4.22____
__1.1____
__383____
__233____
__239____
__122.2____
Scientific Notation
Scientific Notation
• Scientists have developed a shorter method to
express very large numbers.
• Scientific Notation is based on powers of the
base number 10.
• 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 1 - 9.99
• 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.
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
Scientific Notation Practice
a)
b)
c)
d)
e)
0.0826
2 630 000
945 000
1 760 000
0.00507
_______________
_______________
_______________
_______________
_______________
a)
b)
c)
d)
e)
1.23 x 10-4
7.51 x 105
3.09 x 10-3
2.91 x 102
9.6 x 104
_______________
_______________
_______________
_______________
_______________
a)
b)
c)
d)
e)
0.0826
2 630 000
945 000
1 760 000
0.00507
__8.26 x 10-2___
__2.63 x 106___
__9.45 x 105___
__1.76 x 106___
__5.07 x 10-3___
a)
b)
c)
d)
e)
1.23 x 10-4
7.51 x 105
3.09 x 10-3
2.91 x 102
9.6 x 104
__0.000123_____
__751000______
__0.00309_____
__291_________
__96000_______