Metric System Basics

MetricsScientists are very lazy, they don’t want to have to remember all of those different conversions.So instead we use the Système International (SI) Its French!Or we can just say the Metric System.Its all based on the number 10.

Metrics - DistanceWhat is Distance?

Definition:The space

between two

points.

Tool:Meter Stick

Ruler

Unit:Meter

(m)

Metrics - VolumeWhat is Volume?

Definition:The amount of

space something takes up.

Tool:Graduated

CylinderRuler

(Length x Width x Height)

Unit:Liter(L)

Metrics - MassWhat is Mass?

Definition:The amount of

stuff (or Matter)

inside an object.

Tool:Electric or Mechanical Balance

Unit:Gram

(g)

Metrics - TemperatureWhat is Temperature?

Definition:How fast the particles of an

object are moving (due

to heat).

Tool:Thermometer. Unit:

Degrees Celsius(oC)

Metrics - Temperature

So remember:0 o Celsius is when water freezes100 o Celsius is when water boils.

Metrics – Powers of Ten

kilo-(K)1000

hecto-

(H)100

 deka-

(D)10 

Liter(L)

Meter(m)

Gram(g)

deci-(d).1

centi-(c).01

milli-(m).001

Metrics – Powers of TenAs we change from different types of measurements, we change our prefix.For example 30 millimeters = 3 centimetersThey are both measures of length, but a millimeter is ten times smaller than a centimeter.Let’s practice a few conversions.

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

Meter-m

Liter-L

Gram-gK

H

Dk

dc

m

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

To convert to a larger unit, move the decimal point to the left or divide:

To convert to a smaller unit, move the decimal point to the right or multiply:

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

Convert 6 cm = _____ mm

We are converting to:

a) larger unit

b) smaller unit

Convert 6 cm = 60 mm

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

Convert 40 mm = _____ cm

We are converting to:

a) larger unit

b) smaller unit

Convert 40 mm = 4 cm

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

Convert 90 cm = _____ m

We are converting to:

a) larger unit

b) smaller unit

Convert 90 cm = 0.9 m

Converting Metrics

kilo

1000 hecto

100 deka

10 Base

Unit deci

1/10 centi

1/100 milli

1/1000

Convert 200 mm = _____ m

We are converting to:

a) larger unit

b) smaller unit

Convert 200 mm = 0.2 m

Converting Metrics

1000 mg = _______________ g

1L = _______________ mL

160 cm = _______________ mm

14 km = _______________ Dm

109 g = _______________ dg

240 m = _______________ cm

1

1000

1600

1400

1090

24,000

Dimensional Analysis

What is Dimensional Analysis?

Dimensional analysis is a problem-solving method that uses the idea that any number or expression can be multiplied by one without changing its value.It is used to go from one unit to another.

How Does Dimensional Analysis Work?

A conversion factor, or a fraction that is equal to one, is used, along with what you’re given, to determine what the new unit will be.

In chemistry, it is often usefulto be able to convert from one

unit of measure to another

For example:mass of a substance converted to thenumber of atoms in that substance,or converting from one metric unitto another metric unit

First we will see how it works with dozen.

You know that a dozen is 12 of something.

If you have 36 donuts,how many dozen donuts do you have?

You want to know how many dozen in 36 donuts,and you know there is 1 dozen per 12 donuts, or 1 dozen12 donuts

Use this relationship to convert fromindividual donuts to dozen donuts:

36 donuts x 1 dozen12 donuts

In the problem how many dozen in 36 donuts,you know there is 1 dozen per 12 donuts, or 1 dozen12 donuts

Use this relationship to convert fromindividual donuts to dozen donuts:

In the problem how many dozen in 36 donuts,you know there is 1 dozen per 12 donuts, or 1 dozen12 donuts

36 donuts x = 1 dozen12 donuts

36 donuts x 1 dozen 12 donuts

Use this relationship to convert fromindividual donuts to dozen donuts:

In the problem how many dozen in 36 donuts,you know there is 1 dozen per 12 donuts, or 1 dozen12 donuts

36 donuts x = 1 dozen12 donuts

36 donuts x 1 dozen 12 donuts

= 36 dozen 12

Use this relationship to convert fromindividual donuts to dozen donuts:

In the problem how many dozen in 36 donuts,you know there is 1 dozen per 12 donuts, or 1 dozen12 donuts

36 donuts x = 1 dozen12 donuts

36 donuts x 1 dozen 12 donuts

= 36 dozen 12

= 3 dozen

Use this relationship to convert fromindividual donuts to dozen donuts:

= 3 dozen36 donuts

If you have 2.5 dozen donuts, how many individualdonuts are there?

2.5 dozen x 12 donuts1 dozen

there are 12 donutsin 1 dozen

If you have 2.5 dozen donuts, how many individualdonuts are there?

2.5 dozen x =12 donuts1 dozen

2.5 dozen x 12 donuts1 dozen

2.5 x 12 donuts1

=

= 30 donuts

Here are the two problems side by side:

2.5 dozen 12 donuts 2.5 dozen x 12 donuts1 dozen 1 dozen

2.5 x 12 donuts 1

30 donuts

x =

=

=

x =36 donuts 1 dozen 36 donuts 1 dozen12 donuts 12 donuts

36 dozen 1

3 dozen

=

=

x

notice the two conversion factorsare reciprocals of each other

2

2.5 dozen 12 donuts 2.5 dozen x 12 donuts1 dozen 1 dozen

2.5 x 12 donuts 1

30 donuts

x =

=

=

x =36 donuts 1 dozen 36 donuts 1 dozen12 donuts 12 donuts

36 dozen 1

3 dozen

=

=

x

12 donuts = 1 dozen

1 dozen12 donuts = 1

12 donuts 1 dozen = 1

2.5 dozen 12 donuts 2.5 dozen x 12 donuts1 dozen 1 dozen

2.5 x 12 donuts 1

30 donuts

x =

=

=

x =36 donuts 1 dozen 36 donuts 1 dozen12 donuts 12 donuts

36 dozen 1

3 dozen

=

=

x

12 donuts = 1 dozen

1 dozen12 donuts

12 donuts 1 dozen = 1

= 1converts

donuts to dozen

2.5 dozen 12 donuts 2.5 dozen x 12 donuts1 dozen 1 dozen

2.5 x 12 donuts 1

30 donuts

x =

=

=

x =36 donuts 1 dozen 36 donuts 1 dozen12 donuts 12 donuts

36 dozen 1

3 dozen

=

=

x

12 donuts = 1 dozen

1 dozen12 donuts

12 donuts 1 dozen = 1

= 1converts

dozen to donuts

Since conversion factors always equal 1,you can multiply them by anything you

want and still end up with the same thingexcept that it will be in a different form

Let’s try converting donut mass to number of donuts…

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

What’s the conversion?

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

1. what is the qestion asking you to convert?

1. what is the qestion asking you to convert?

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

grams to donuts

2. what is the relationship between grams and donuts?

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

2. what is the relationship between grams and donuts?

150 grams = 1 donut

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

3. set up the conversion factors:

150 g = 1 donut

so…

and

150 g1 donut

= 1

1 donut150 g = 1

150 g = 1 donut

150 g1 donut

= 1

1 donut150 g = 1

these are yourconversion factors

150 g = 1 donut

150 g1 donut

= 1

1 donut150 g = 1

converts donuts tograms (grams on top)

150 g = 1 donut

150 g1 donut

= 1

1 donut150 g = 1

converts grams todonuts (donuts on top)

The question is…

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

The question is…

9900 gram s

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

9900 grams

begin with the amountgiven in the problem

The question is…

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

9900 gram s

The question is…

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

9900 gram s

each donut has a mass of 150 grams

The question is…

x9900 gram s 1 donut150 grams

converts gramsto donuts

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?each donut has a mass of 150 grams

The question is…

x9900 gram s 1 donut150 grams

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?

9900 donuts 150

66 donuts

=

= 66 donuts

The question is…

x9900 gram s 1 donut150 grams

x=

9900 g 1 donut150 g

If you have 9900 grams of donuts,how many donuts do you have

if each donut has a mass of 150 grams?how many donuts do you have

9900 gram s = 66 donuts

Examples of Conversions

60 s = 1 min60 min = 1 h24 h = 1 day

Examples of Conversions

You can write any conversion as a fraction.Be careful how you write that fraction.For example, you can write

60 s = 1 min as 60s or 1 min 1 min 60 s

Examples of Conversions

Again, just be careful how you write the fraction. The fraction must be written so that like units cancel.

Steps

1. Start with the given value.2. Write the multiplication symbol.3. Choose the appropriate conversion

factor.4. The problem is solved by multiplying

the given data & their units by the appropriate unit factors so that the desired units remain.

5. Remember, cancel like units.

Let’s try some examples together…

1. Suppose there are 12 slices of pizza in one pizza. How many slices are in 7 pizzas?

Given: 7 pizzasWant: # of slices

Conversion: 12 slices = one pizza

7 pizzas1

SolutionCheck your work…

X 12 slices1 pizza = 84 slices

Let’s try some examples together…

2. How old are you in days?

Given: 17 yearsWant: # of days

Conversion: 365 days = one year

Solution

Check your work…

17 years1

X 365 days1 year = 6052 days

Let’s try some examples together…

3. There are 2.54 cm in one inch. How many inches are in 17.3 cm?

Given: 17.3 cmWant: # of inches

Conversion: 2.54 cm = one inch

SolutionCheck your work…

17.3 cm1

X1 inch

2.54 cm = 6.81 inches

Be careful!!! The fraction bar means divide.

Now, you try…1. Determine the number of eggs in 23

dozen eggs.

2. If one package of gum has 10 pieces, how many pieces are in 0.023 packages of gum?

Multiple-Step Problems

Most problems are not simple one-step solutions. Sometimes, you will have to perform multiple conversions.Example: How old are you in hours?

Given: 17 yearsWant: # of days

Conversion #1: 365 days = one yearConversion #2: 24 hours = one day

SolutionCheck your work…

17 years1

X365 days

1 year X24 hours

1 day = 148,920 hours