Transcript The Metric System

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 Units
Quantity
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?
1
 1m 


0.054 m  100 cm 
0.054 m  1 m 


1
 100cm 
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.
2.
Read the problem carefully and
highlight any numbers and their units.
Determine what is known and what is
to be solved for.
Plan out your course of action. What
conversion factors are needed? Write
them down.
Problem-Solving
3.
4.
5.
Set-up and organize the problem in a
neat and logical fashion making sure
units cancel for each step.
Calculate your answer following
proper mathematics and round to the
proper number of significant digits.
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
mass of the substance to its D  Volume
volume.
 A substance can sometimes
be identified by its density.
 Standard units for solids and
liquids are grams per
milliliter.

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.?