Standards of Measurements Chapter 1.2
Dec 28, 2015
Standards of Measurements
Chapter 1.2
Accuracy and Precision
Accuracy – how close a measured value is to the actual value
Precision – how close the measured values are to each other
Significant Figures
All nonzero digits are significant. 1, 2, 3, 4, 5, 6, 7, 8, 9
Zeros within a number are always significant. Both 4308 and 40.05 have four significant figures.
Significant Figures
Zeros that set the decimal point are not significant. 470,000 has two significant figures.
Trailing zeros that aren't needed to hold the decimal point are significant. 4.00 has three significant figures.
Significant Figures
If the least precise measurement in a calculation has three significant figures, then the calculated answer can have at most three significant figures.
Mass = 34.73 grams Volume = 4.42 cubic centimeters.
Rounding to three significant figures, the density is 7.86 grams per cubic centimeter.
Scientific Notation
For large numbers, moving the decimal to the left will result in a positive number 346500 = 3.46 x 105
For small numbers, moving the decimal to the right will result in a negative number 0.000145 = 1.45 x 10-4
For numbers less than 1 that are written in scientific notation, the exponent is negative.
Scientific Notation
Before numbers in scientific notation can be added or subtracted, the exponents must be equal. 5.32 x 105 + 9.22 x 104
5.32 x 105 + 0.922 x 105
5.32 + 0.922 x 105
6.24 x 105
Scientific Notation
When numbers in scientific notation are multiplied, only the number is multiplied. The exponents are added.
(3.33 x 102) (2.71 x 104) (3.33) (2.71) x 102+4
9.02 x 106
Scientific Notation
When numbers in scientific notation are divided, only the number is divided. The exponents are subtracted.
4.01 x 109
1.09 x 102
4.01 x 109-2
1.09
3.67 x 107
Scientific Notation
A rectangular parking lot has a length of 1.1 × 103 meters and a width of 2.4 × 103 meters. What is the area of the parking lot?
(1.1 x 103 m) (2.4 x 103 m) (1.1 x 2.4) (10 3+3) (m x m) 2.6 x 106 m2
SI Units
Kilo- (k)
1000
Milli- (m)
Hecto- (h)
Deka- (da)
Base Unit
Deci- (d)
Centi- (c)
100
10
m, L, g
0.1
0.01
0.001Mnemonic device:
King Henry Died By Drinking Chocolate Milk
Metric System
Meter (m) – The basic unit of length in the metric system
Length – the distance from one point to another A meter is slightly longer
than a yard
Metric System
Liter (L) – the basic unit of volume in the metric system A liter is almost equal to a
quart
Metric System
Gram (g) – The basic unit of mass
Derived Units
Combination of base units Volume – length width height
1 cm3 = 1 mL Density – mass per unit volume (g/cm3)
D = MV D
M
V
Density
1) An object has a volume of 825 cm3 and a density of 13.6 g/cm3. Find its mass.
GIVEN:
V = 825 cm3
D = 13.6 g/cm3
M = ?
WORK:
M = DV
M = 13.6 g x 825 cm3
cm3 1
M = 11,220 gDM
V
Density
2) A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
GIVEN:
D = 0.87 g/mL
V = ?
M = 25 g
DM
V
WORK:
V = M D
V = 25 g
0.87 g/mL
V = 28.7 mL
Density
3) You have a sample with a mass of 620 g & a volume of 753 cm3. Find the density.
GIVEN:
M = 620 g
V = 753 cm3
D = ?
DM
V
WORK:
D = M V
D = 620 g
753 cm3
D = 0.82 g/cm3
Unit Factors
Slopes
Percentage Error
Temperature
A degree Celsius is almost twice as large as a degree Fahrenheit.
You can convert from one scale to the other by using one of the following formulas:
Temperature
Convert 90 degrees Fahrenheit to Celsius oC = 5/9 (oF - 32)
oC = 5/9 (90 - 32)
oC = 0.55555555555555556 (58)
oC = 32.2
Temperature
Convert 50 degrees Celsius to Fahrenheit oF = 9/5 (oC ) + 32
oF = 9/5 (50 ) + 32
oF = 1.8 (50) + 32
oF = 90 + 32
oF = 122
Temperature
The SI base unit for temperature is the kelvin (K). • A temperature of 0 K, or 0 kelvin, refers to the
lowest possible temperature that can be reached. • In degrees Celsius, this temperature is
–273.15°C. To convert between kelvins and degrees Celsius, use the formula:
Temperature