The Metric System

A decimal system of units for measurements of length, mass, time, etc.

System International (SI) units – a superset of seven units from which all others can be derived.

SI UnitsQuantity Name of Unit Abbreviation

Length meter m

Mass kilogram kg

Temperature kelvin K

Time second s

Amount of Substance mole mol

Electric current ampere A

Luminous intensity candela cd

Common Prefixes

Prefix Symbol Numerical Value

Mega M 1,000,000 = 1 x 106

kilo k 1,000 = 1 x 103

centi c 0.01 = 1 x 10-2

milli m 0.001 = 1 x 10-3

micro m 0.000001 = 1 x 10-6

Conversion Factor

A relationship between two quantities. Important – both quantities should

include units. Can be:

– metric-to-metric.– English-to-English.– English-to-metric.

Conversion Factor

1 foot = 12 inches

100 cm = 1 m

1 inch = 2.54 cm

Dimensional Analysis

Uses units with the numerical values. All units should cancel except those that

are desired for the answer. My method is sometimes referred to as

the “fence-post” method. Remember – answers should be

rounded to the proper number of significant figures!

Dimensional Analysis

Ex) 45 inches = ? centimeters

Dimensional Analysis

0.054 meters = ? centimeters

Why are these set-ups wrong?

cm 100

m 1

m 054.0

1

cm 100

m 1

1

m 054.0

Dimensional Analysis

Multi-step problems can be done either all at once or one step at a time.

Ex) 2.50 feet = ? cm

Problem-Solving

1. Read the problem carefully and highlight any numbers and their units. Determine what is known and what is to be solved for.

2. Plan out your course of action. What conversion factors are needed? Write them down.

Problem-Solving

3. Set-up and organize the problem in a neat and logical fashion making sure units cancel for each step.

4. Calculate your answer following proper mathematics and round to the proper number of significant digits.

5. Check your answer and work.

Dimensional Analysis

Ex) 15 pints = ? L

Dimensional Analysis

55 miles per hour = ? meters per second

How long will it take to travel 5.0 km at this speed?

Measuring Mass and Volume

Matter = anything that occupies space and has mass.

The SI unit of mass is the kilogram. Volume is a derived unit and is the

amount of space occupied by matter. Based on the SI system, the standard

unit would be a meter x meter x meter or cubic meter (m3).

Measuring Mass and Volume

However, this is too large to use in practical uses.

1 milliliter (mL) is defined as a cube that measures 1 cm x 1 cm x 1 cm.

Thus, 1 mL = 1 cm3 or 1 cc.

Volume Conversions

A block measures 12 inches by 6.5 inches by 2.5 inches. What is the volume of this block in Liters?

Temperature

Temperature is the measurement of the amount of heat a substance has.

Heat flows from warmer to colder objects.

SI unit is the Kelvin. Metric unit is Celsius. English unit is Fahrenheit.

Temperature Conversions

oF = (1.8 x oC) + 32

oC = (oF – 32) / 1.8

K = oC + 273.15

Temperature Conversions

Convert 72oC to Fahrenheit

Convert 65oF to Celsius

Convert 225K to Fahrenheit

Density

Density is the ratio of the mass of the substance to its volume.

A substance can sometimes be identified by its density.

Standard units for solids and liquids are grams per milliliter.

Volume

mass D

Density

Can use the density of a substance as a conversion factor.

Density of Aluminum = 2.70 g/mL. Thus, every 1 mL of Al = 2.70 g. What volume would a mass of a 452

gram block of Al occupy?

Density

A 2.50 gallon container of a liquid has a mass of 16.7 pounds. What is the density of the liquid in grams per milliliter?

Density

The density of gold is 19.3 g/mL. What is the mass in grams of a gold bar measuring 6.0 in. x 4.0 in. x 2.0 in.?