Transcript 8.uncertaintyandsignificant

8
Significant
Figures
Significant figures
The number of meaningful digits in a measurement including the
uncertain digit.
“sig figs”
0.520
0.0025
500
0.02300
120035
500.
2.0 x 105
3
2
1
4
6
3
2
do not count zeros at the beginning
do not count end zeros if no decimal
count all other zeros
do not expand
Significant figures
The number of meaningful digits in a measurement including the
uncertain digit.
“sig figs”
5
2.5002
0.00650
3
5001
4
0.0200300
6
4
0.02010
1
200
200.
3
2.0 x 102
2
2. x 102
1
Significant figures
Exact numbers that are counted or defined and not measured have zero
uncertainty and infinite “sig figs”.
“sig figs”
2.50 cm
3 girls
62.33 kJ
1 cm = 10 mm
12.3 oC
200 lb
1 cm3 = 1 mL
$75.00
3
infinite
4
infinite
3
1
infinite
infinite
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
1.
+
21.036
22.1
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
1.
+
21.036
22.1??
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
1.
+
=
21.036
22.1??
43.1
the largest decimal place is the first
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
2.
=
25.654
22.1??
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
2.
=
25.654
22.1??
3.6
the largest decimal place is the first
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
3.
-
301.2256
0.36
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
3.
-
301.2256
0.36
300.87
the largest decimal is the second
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used
4.
+
8.053 x 107
2.3 x 104
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
4.
+
8.053 x 107
2.3 x 104
↓ largest decimal place
80530000.
23000.
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
4.
+
8.053 x 107
2.3 x 104
8.055 x 107
↓ largest decimal place
80530000.
23000.
80550000.
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
5.
+
2.463 x 10-5
5.006 x 10-2
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
5.
+
2.463 x 10-5
5.006 x 10-2
0.00002463
0.05006
↑
largest decimal place
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
5.
+
2.463 x 10-5
5.006 x 10-2
5.008 x 10-2
0.00002463
0.05006
0.05008
largest decimal place
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
6.
-
5.331 x 10-4
2.126 x 10-5
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
6.
-
5.331 x 10-4
2.126 x 10-5
↓ largest decimal place
0.0005331
0.00002126
Adding and Subtraction with Significant Figures
When adding or subtracting numbers round the answer to
the largest decimal place found in the uncertain digits of any
of the numbers used.
6.
-
5.331 x 10-4
2.126 x 10-5
5.118 x 10-4
↓ largest decimal place
0.0005331
0.00002126
0.0005118
7. Add the two numbers- another way to do it
2.657 x 10-12
0.027 x 10-12
2.684 x 10-12
2.657 x 10-14
0.02657 x 10-12
Change the lower exponent to the higher and write it directly
underneath.
You are making the exponent larger so make the number smaller.
8. Subtract the two numbers- another way to do it
8.9967 x 1018
- 0.0053 x 1018
8.9914 x 1018
- 5.222 x 1015
0.005292 x 1018
Change the lower exponent to the higher and write it directly
underneath.
You are making the exponent larger so make the number smaller.