Metric System Basics

Metrics Scientists 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 - Distance What is Distance? Definition: The space between two points. Tool: Meter Stick Ruler Unit: Meter (m)

Metrics - Volume What is Volume? Definition: The amount of space something takes up. Tool: Graduated Cylinder Ruler (Length x Width x Height) Unit: Liter (L)

Metrics - Mass What is Mass? Definition: The amount of stuff (or Matter) inside an object. Tool: Electric or Mechanical Balance Unit: Gram (g)

Metrics - Temperature What is Temperature? Definition: How fast the particles of an object are moving (due to heat). Tool: Thermometer. Unit: Degrees Celsius ( o C)

Metrics - Temperature So remember: 0 o Celsius is when water freezes 100 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 Ten As we change from different types of measurements, we change our prefix. For example 30 millimeters = 3 centimeters They 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-g K H Dk d c 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 ,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 useful to be able to convert from one unit of measure to another For example: mass of a substance converted to the number of atoms in that substance, or converting from one metric unit to 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 dozen 12 donuts Use this relationship to convert from individual donuts to dozen donuts:

36 donuts x 1 dozen 12 donuts In the problem how many dozen in 36 donuts, you know there is 1 dozen per 12 donuts, or 1 dozen 12 donuts Use this relationship to convert from individual donuts to dozen donuts:

In the problem how many dozen in 36 donuts, you know there is 1 dozen per 12 donuts, or 1 dozen 12 donuts 36 donuts x = 1 dozen 12 donuts 36 donuts x 1 dozen 12 donuts Use this relationship to convert from individual donuts to dozen donuts:

In the problem how many dozen in 36 donuts, you know there is 1 dozen per 12 donuts, or 1 dozen 12 donuts 36 donuts x = 1 dozen 12 donuts 36 donuts x 1 dozen 12 donuts = 36 dozen 12 Use this relationship to convert from individual donuts to dozen donuts:

In the problem how many dozen in 36 donuts, you know there is 1 dozen per 12 donuts, or 1 dozen 12 donuts 36 donuts x = 1 dozen 12 donuts 36 donuts x 1 dozen 12 donuts = 36 dozen 12 = 3 dozen Use this relationship to convert from individual donuts to dozen donuts:

= 3 dozen 36 donuts

If you have 2.5 dozen donuts, how many individual donuts are there? 2.5 dozen x 12 donuts 1 dozen there are 12 donuts in 1 dozen

If you have 2.5 dozen donuts, how many individual donuts are there? 2.5 dozen x= 12 donuts 1 dozen 2.5 dozen x 12 donuts 1 dozen 2.5 x 12 donuts 1 = = 30 donuts

Here are the two problems side by side: notice the two conversion factors are reciprocals of each other 2

12 donuts = 1 dozen 1 dozen 12 donuts = 1 12 donuts 1 dozen = 1

12 donuts = 1 dozen 1 dozen 12 donuts 1 dozen = 1 converts donuts to dozen

12 donuts = 1 dozen 1 dozen 12 donuts 1 dozen = 1 converts dozen to donuts

Since conversion factors always equal 1, you can multiply them by anything you want and still end up with the same thing except 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?

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 g 1 donut = 1 1 donut 150 g = 1

150 g = 1 donut 150 g 1 donut = 1 1 donut 150 g = 1 these are your conversion factors

150 g = 1 donut 150 g 1 donut = 1 1 donut 150 g = 1 converts donuts to grams (grams on top)

150 g = 1 donut 150 g 1 donut = 1 1 donut 150 g = 1 converts grams to donuts (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… 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 amount given 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?

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? each donut has a mass of 150 grams

The question is… converts grams to 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… 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… 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

=

Examples of Conversions 60 s = 1 min 60 min = 1 h 24 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 pizzas Want: # of slices Conversion: 12 slices = one pizza

7 pizzas 1 Solution Check your work… X 12 slices 1 pizza = 84 slices

Let’s try some examples together… 2. How old are you in days? Given: 17 years Want: # of days Conversion: 365 days = one year

Solution Check your work… 17 years 1 X 365 days 1 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 cm Want: # of inches Conversion: 2.54 cm = one inch

Solution Check your work… 17.3 cm 1 X 1 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 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 years Want: # of days Conversion #1: 365 days = one year Conversion #2: 24 hours = one day

Solution Check your work… 17 years 1 X 365 days 1 year X 24 hours 1 day = 148,920 hours