Transcript Significant Figures

The Use of Measurement
Think of a world without
measurement of any kind, qualitative
or quantitative.
 In measurement we have what are
called Base units and Derived units
(density = g/ml).

BASE UNITS
Time: the SI base unit is second (s)
 Length: the SI base unit is meter
(m)
 Mass: the SI base unit is the
kilogram (kg)

DENSITY
 Density is a ratio that compares the mass
of an object to its volume.
 The units for density are often grams per
cubic centimeter (g/cm3)
 Density = Mass
Volume
Accuracy vs Precision
Accuracy is how close your answers are
to the correct answer.
 Precision is how close your individual
answers are to each other.
 Can you have good precision and bad
accuracy?

Measurement involves
numbers and calculations.
When taking measurements, you are limited to the
“accuracy” of your equipment.
 Some measurements may be precise, but not
accurate. What’s the difference?
 Three readings:
13.355 g
13.655 g
13.455 g
If the correct answer is 13.653 g, what would you say
about the accuracy? Precision?

Conversions
Kilo (K)
Hecta (H)
Deka (D)
gram/liter/meter
deci (d)
centi (c)
milli (m)
Conversions
• Determine where you are in the staircase and where
you need to be. The number of steps you take will
tell you how many places to move the decimal and in
what direction
Ex. Convert 125 cg to _____kg
Solution: To go from cg to kg, we will take 5 steps to
the left (up). This means we will move the decimal 5
places to the left; i.e., 125 cg becomes 0.00125 kg.
Scientific Notation
(how to deal with really big & small numbers)
If you were asked to multiply .00000068 x 9800000,
you’d be upset. Why?

SN is a way to deal with large & small numbers by using
exponents to take care of the zeros.
ex.
.00000068 = 6.8 x 10 -7
9800000 = 9.8 x 10 6
Simply move the decimal pt. until you have 1 sig.fig. to the left
of it.
1. Count the number of places you moved. That’s your
exponent!
2. If you moved the pt. to the left, the sign is positive; moved
it right, and the sign is negative.
3. 512000 = 5.12 x 10 5
&
0.0000512 = 5.12 x 10 -5

Scientific Notation


When adding or subtracting two or more numbers that
are in scientific notation, the exponents must be the
same. (Think of having a common denominator)
When multiplying two or more numbers in scientific
notation, the exponents are added.
ex. (7 x 105) x (6 x 109) = 42 x 1014 = 4.2 x 1015
 When dividing two numbers in scientific notation, the
bottom exponent is subtracted from the top exponent.
ex. 8 x 108/4 x 105 = 2 x 103
Calculations for S.N.
Use your calculator!
 (4.2 x 106)(3.5 x 103) =
 (2.5x 103)(3.5 x 10-4) =
 2.6 x 104
1.2 x 10 -4
=
(3.5x105)(2.54x10-2)
(4.2x10-2)(5.63x103) =
Now, what do we do with all those Insignificant numbers our calculator gives
us?
Your answer is limited in significant figures to the least number in any one
part of the problems.