Significant Figures
Topics
Notes
Exact Values / Numbers
exact values - anything that we can count, values that are known exactly
conversion factors are also exact values
Measured Values
With any measured values, there is some degree of uncertainty
uncertainty varies with instrumentation, also with ability to interpret
value accurately and precisely
Measured values are anything we measure, these values are inexact
Will consist of certain numbers and uncertain numbers.
Digits with 100% confidence and others that are harder to report,
depending on how it is interpreted
Always report certain numbers, and estimate one place to the right of
the last certain digit. (Ex. Must be between 17 and 18, estimate 17.1)
Last digit is uncertain, but certain number is agreed upon
Digital Device + Significant Figures
SF - estimate of uncertainty or tolerance (precision)
Last digit of digital device is uncertain
Instrumentation has varying levels of precision, depending on
number of significant figures
Lots of decimal places (more precise)
Significant Figures Rules
Significant:
Non-zero numbers (75.7 C = 3 SF)
Interior zeros (sandwiched between 2 non-zero digits)
Trailing zeros (zeros at end of number IF number has decimal)
Ex. 55.220 = 5 SF
No decimal? - 34,200 = ? SF Ambiguous Number
(needs decimal at the end, will be marked incorrect)
NOT Significant:
Leading zeros (0.00661 = 3 SF (or 6.61 x 10^-3, best
expressed in scientific notation)
Scientific Notation
47000 in scientific notation is 4.7 x 10^4
exp positive, move decimal to the left
exp negative, move decimal place to the right
Scientific Notation and Sig
Figs
30. = 2 sig figs = 3.0 x 10^1
0.3 = 1 sig fig = 3 x 10^-1
150 = 3 sig figs = 1.5 x 10^2
0.046 = 2 sig figs = 4.6 x 10^-2
60,367 = 5 sig figs = 6.0367 x 10^4
Math for the Masses
Calculation and Significant
Figures
Addition and Subtraction
Round final answer to the least number of decimal places
125.16 + 129. + 25.20 = 306.37 but 306, 0 decimal places but
3 sig figs = 3.06 x 10^2
Multiplication and Division
Round final answer to the least number of significant figures
5.68 x 10.01 = 56.8568 rounded to 56.9
Round as our last mathematical step
Density Calculations
Classifying Matter by
Composition: Elements,
Compounds, and Mixtures
Can measure density of an object based on displacement
Mass of gold sample = 51.842 g
Initial Volume of water = 17.1 mL
Final Volume of water = 19.8 mL
Volume of gold sample = 2.7 mL
Density = 51.842g (mass) / 2.7 mL (volume) = 19 g/mL