What is a significant figure?

• Significant figures in a measurement consist of all the digits known with certainty plus one final digit that is estimated.

• Your answer can only be as accurate as your least accurate measurement.

How do I determine the number of significant figures?

• All non-zero numbers are significant (Only determine if significant for 0’s).

• Zeros in FRONT of significant numbers are NOT significant. EX. 0.0095897

• Zeros BEHIND significant numbers when a decimal is present ARE significant. Ex. 85.00

• Zeros BEHIND significant numbers when a decimal is not present are NOT significant. Ex. 85000. (This is an estimate, zeros are placeholders).

• Zeros in between significant numbers are significant.

SIG FIGS

14550000.01120.12500014500.14005326.50 X 104

1.4200 X 1010

Rules for Multiplying and DividingHow many sig figs go in answer?

• The number of sig figs in product (or quotient) should equal the LEAST number of sig figs in problem.

• Ex.– (7.21)(1.245)=– (6.6)/(2.2) =– (3.4 X 109)(2.3 X 102)=

Adding and Subtracting with Sig Figs

• The number of sig figs in the answer will depend on the number of digits past the decimal. When the numbers are aligned with the decimal, the answer will be the same as the least number of decimal places.

• Ex.

Percent Error• Percent error is used to compare the experimental

data to its true value to determine accuracy.

• Formula:• % error=experimental value – accepted value X 100

accepted value

Experimental data– data obtained from experimentAccepted value—value believed to be true (CRC Handbook

of Physics and Chemistry)

Example:

• What is the percentage error for a mass measurement of 17.7g, given the correct value of 21.2g?

• A volume is measured experimentally as 4.26 mL. What is the percentage error, given that the correct value is 4.15 mL?

Measurement

• Measurements represent quantities. A quantity has magnitude, size, or amount.

• Scientists use the SI system of measurement, called the Le Systeme International d’Unites. Aka metrics. This system was adopted in 1960. SI now has 7 base units, and most other units are derived from these 7.

Quantity symbol

unit Unit abbrev.

definition tool

length l meter

m The length of the path traveled by light in a vacuum during a time interval of 1/299792458 second. (Distance between 2 points)

meterstick

mass m kilogram

kg The amount of matter in an object Triple beam balance

time t second

s Interval between 2 events stopwatch

Tempera-ture

T kelvin K How hot or cold an object isoC + 273.15

thermometer

amount n mole mol 6.02 X 1023 particles Usually triple beam balance

Volume- liquid

liter l The amount of space occupied by an object

Graduated cylinder

Volume-solid

Cubic centi-meters

cm3 or cc

Length X width X height meterstick

Mass vs. Weight

• Mass is a measure of the quantity of matter.• Weight is a measure of the gravitational pull on

matter.• Mass does not depend on gravity; weight does.• Mass is measured with a balance, weight is

measured with a spring scale.• On Earth, weight increases as mass increases.

The weight of an object on the moon is about 1/6 of its weight on Earth.

Derived Units

• Derived units are combinations of 2 or more base units. They are produced by multiplying or dividing standard units.

• Examples: area, volume, density, energy, pressure.• Density is mass/volume, so divide an objects mass

by its volume. The unit will be g/ml, a derived unit.

• Volume is l X w X h, so unit is cm3 or cmX cmX cm.

Metric Conversions