Chapter 2 notes
Objectives:
Express numbers in scientific notation
Convert numbers written in scientific notation to decimal notation
Determine the number of significant figures in a given number or measurement
Difference between an exact number and measured number
Report measured quantities to correct number of significant figures in calculation
Learn about seven basic units and use of dimensional analysis to convert one unit to another unit
Scientific Notation:
Measurements are associated with very large numbers ( 14,000,000,000,000 meters) or very small
numbers( 0.000000000001 seconds)
Scientific notation can be used to write these numbers more compactly
A number written in scientific notation consists of a decimal par and an exponential part
The decimal part is a number between 1 and 10
The exponential part is 10 raised to an exponent
1.2 x 105
Expressing the numbers in scientific notation
36,458,000
0.000987
1,286,000
44.550000
19,307,000
0.0000015
514,000
0.00786
Expressing the numbers in decimal notation
3.89 x 109
1.2 x 10-2
8.76 x 1011
6.6 x 10-1
9.95 x 10-5
2.99 x 102
Uncertainty in measurement
Uncertainty always exist in measures quantities because of
a) Limitation in measuring device
b) Visual estimation by an individual
Measuring devices commonly used in chemistry lab
Balance to find mass of a substance ( kg, g ,cg, mg, µg, ng, pg)
200.0g
200.08g
200.086g
200.0864g
Meter stick and a ruler to find length( km, m, cm, mm, µm, nm, pm)
12.25 cm
12.25 m
Graduated cylinder to find volume( kL, L, cL, mL, µL, nL, pL)
12.5 mL
20.0 mL
Thermometer to find temperature ( ℃ , ℉ , K)
25.0 ℃
23.3 ℃
All certain digits and the last digit ( estimated) are called significant figures.
Uncertainty in the last digit is reported as ± 1
Uncertainty in the measurements
1.20 g ±
121g ±
15. 593 g ±
11.2 g ±
Rules for counting significant figures:
Nonzero digits are always significant
186
2365
56897
1234567
There are three types of zeros
a) Leading zeros to the right of the decimal point that precede ( come before) all the nonzero digits
0.0087
0.0125
0.000023
0.000001
Captive zeros are always significant and they fall between nonzero digits.
4.0008
2.908038
32.0081
Trailing zeros are at the right end of a number. They are significant only if number is written with a
decimal point
100
100.
100.0
100.00
1200
1200.
12.20
Exact numbers have unlimited number of significant figures. Exact numbers originate from three
sources:
Accurate counting of discrete objects, defined quantities, integral numbers that are part of an equation.
8 apples
1 in. = 2.54 cm
radius = diameter/2
Rounding of numbers
To show your answer to correct number of sig.figs you need to round off your answer
13.35 → 3 sig. figs
13. 34 → 3 sig.figs
Round off these numbers to three sig.figs
251.904
0.00985643
3. 9999
5.535691 x 10-7