CHEM Significant Figures
To be in proper scientific notation the number must be written with:
- a number between 1 & 10 - multiply by a power of 10
What is the density of a 12.5 mL aqueous solution that has a mass of 10.081 g?
.8
Which of the following measurements contains three significant figures? 0.01 g 0.010 g 0.01010 g 0.0100 g
0.0100 g (trailing zeros to the right are significant if there is a decimal point)
A student calculated a length measurement to be 0.06748 cm. What is this length rounded to three significant digits? 0.0674 cm 0.07 cm 0.0675 cm 0.068 cm
0.0675 cm
1 L = ____ dm^3
1
1 mL = ___ cm^3
1
1 meter = ___ cm
100
1 L = ____ mL
1000
1 kg = ____ g
1000
Using the rules for significant figures, the sum of 12.04 liters and 1.091 liters should be expressed as ____ 13.10 liters 13.131 liters 13.1 liters 13.13 liters
13.13 liters
29 kg = ____ g
29000
Find how many minutes a woman has lived by her 35th birthday using dimensional analysis
35 y (360d/1y)(24h/1d)(60m/1h) 35 x 360 x 24 x 60 = 1839600 = 1.84 x 10^7
Which of the following choices has the greatest number of significant figures? 5.050 g 51.0 g 50.050 g 505000 g
50.050 g
How many significant figures are there in each of the following data? 23,486.5 41.200 0.0085 30.61
6 5 2 4
Find how many centimeters are in 6.51 miles using dimensional analysis (1 mile = 5280 feet, 1 ft = 12 in, 1 in = 2.54 cm)
6.51m (5280 ft/1 m)(12 in/1 ft)(2.54cm/1 in) 6.51 x 5280 x 12 x 2.54 = 1047682.944 = 1.05 x 10^6
7100 cm = ____ m
71
Write the following numbers in scientific notation: .000882 .00000059 .00004
8.82 x 10^-4 5.9 x 10^-7 4 x 10^-5
When are zeros significant and when are they place holders?
80.00 has 4 sig figs 41,200 has 3 sig figs
When are numbers exact, and when do they contain uncertainty?
A measurement is exact when there are no zeros to the right of the decimal place. Measurements are uncertain because they are estimations and have margins of error.
prefix, power, abbreviation 1 hundredth
Centi 10 ^ -2
prefix, power, abbreviation 1 tenth
Deci 10 ^ -1 d
What are random errors?
Errors due to a lack of consistency or precision
What are systematic errors?
Errors resulting from making the same mistake for every trial
prefix, power, abbreviation 1 millionth
Micro 10 ^ -6 μ
prefix, power, abbreviation 1 thousandth
Milli 10 ^ -3 m
prefix, power, abbreviation 1 billionth
Nano 10 ^-9 n
What are significant figures? How do they imply the uncertainty of a measurement?
Sigificant figures are all of the certain digits and exactly one uncertain digit
How do you organize data, present it and analyze it?
Tables, graphs, ANOVA and T-tests
How is uncertainty in a measurement expressed explicitly? Implicitly?
Uncertainty can be shown using a plus or minus sign, or using vocabulary: about, roughly, approximately etc
How is percent error calculated?
absolute value of ((experimental value - actual value)/actual value) x 10^2
What are significant figures?
all of the certain digits and exactly one uncertain digit
prefix, power, abbreviation ten
deca 10 D
prefix, power, abbreviation billion
giga 10 ^9 G
prefix, power, abbreviation hundred
hecto 10 ^ 2 H
prefix, power, abbreviation thousand
kilo 10 ^ 3 K
How do we know the quality of data?
larger number of significant figures = more precision
How do we communicate uncertainty?
margin of error - the last digit recorded, plus or minus notation
prefix, power, abbreviation million
mega 10 ^6 M
prefix, power, abbreviation trillionth
pico 10 ^ -12 p
How do we measure volume?
record number at bottom of meniscus plus one digit
What is accuracy?
the closeness of data to the accepted value
What is precision?
the reproducibility of a set of data
An estimate is only as good as...
the tool and the method used
How are all measurements made?
using a measuring tools to compare
