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Metric System & Scientific Notation

ChemistryAugust 20th/21st, 2009

+ Metric System

The metric system is based on a base unit that corresponds to a certain kind of measurement

Length = meter Volume = liter Weight (Mass) = gram

Prefixes plus base units make up the metric system Example:

Centi + meter = Centimeter Kilo + liter = Kiloliter

+ Metric System

The three prefixes that we will use the most are: Kilo= 1000 centi = 1/100 (one hundredth) milli= 1/1000 (one thousandth)

How do you remember all of them? Kissing Hairy Dark space dogs causes mono

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

+ Metric System So if you needed to measure length you would choose meter as your base unit Length of a tree branch

1.5 meters Length of a room

5 meters

But what if you need to measure a longer distance, like from your house to school? Let’s say you live approximately 10 miles from school

10 miles = 16093 meters 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

+ Typical Metric Units

What metric unit would you use to measure the length of the room?

What metric unit would you use to measure the distance between the mall and school?

What metric unit would you use to measure your weight?

What metric unit would you use to measure the amount of liquid in a soda bottle?

What unit would you use to measure the amount of liquid in an eye dropper?

+ Metric System

These prefixes are based on powers of 10. What does this mean? From each prefix every “step” is either:

10 times larger or

10 times smaller For example

Centimeters are 10 times larger than millimeters

1 centimeter = 10 millimeters

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

+ Metric System

Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters

Example not to scale

1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm 1 mm

1 cm

40

41

41

40

+ Metric System

For each “step” to right, you are multiplying by 10

For example, let’s go from a base unit to centi1 liter = 10 deciliters = 100 centiliters

2 grams = 20 decigrams = 200 centigrams

( 1 x 10 = 10) = (10 x 10 = 100)

(2 x 10 = 20) = (20 x 10 = 200)

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

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Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Metric System

An easy way to move within the metric system is by moving the decimal point one place for each “step” desired

Example: change meters to centimeters

1 meter = 10 decimeters = 100 centimetersor1.00 meter = 10.0 decimeters = 100. centimeters

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Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Metric System

Now let’s try our previous example from meters to kilometers:16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers

So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below)

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Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Metric System

If you move to the left in the diagram, move the decimal to the left

If you move to the right in the diagram, move the decimal to the right

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Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Metric System

Now let’s start from centimeters and convert to kilometers

400000 centimeters = ? kilometers

+

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

Metric SystemNow let’s start from meters and convert to centimeters

5 meters = ? centimeters

• Now let’s start from kilometers and convert to meters

.3 kilometers = ? meters

+ Metric System

SummaryBase units in the metric system are meter, liter, gram

Metric system is based on powers of 10For conversions within the metric system, each “step” is 1 decimal place to the right or left

Using the diagram below, converting to the right, moves the decimal to the right and vice versa

Kilo(1000)

Hecto(100)

Deca(10)

Base Units

metergramliter

deci(1/10)

centi(1/100)

milli(1/1000)

+ Scientific Notation

Scientific notation is a way of expressing Scientific notation is a way of expressing really big numbers or really small numbers.really big numbers or really small numbers.

For very large and very small numbers, For very large and very small numbers, scientific notation is more concise.scientific notation is more concise.

Scientific Notation always has two parts: A number between 1 and 9.9999…A number between 1 and 9.9999… A power of 10A power of 10

N x 10N x 10xx

+ Writing Scientific Notation Place the decimal point so that there is Place the decimal point so that there is oneone non-zero digit to the left of the decimal point.non-zero digit to the left of the decimal point.

Count the number of decimal places the decimal Count the number of decimal places the decimal point has “moved” from the original number. point has “moved” from the original number. This will be the exponent on the 10.This will be the exponent on the 10.

If the original number was less than 1, then the If the original number was less than 1, then the exponent is negative. If the original number exponent is negative. If the original number was greater than 1, then the exponent is was greater than 1, then the exponent is positive.positive.

Example: Given: 289,800,000Given: 289,800,000 Start with: 2.898 Start with: 2.898 Decimal needs to move 8 places to the leftDecimal needs to move 8 places to the left Answer: Answer: 2.898 x 102.898 x 1088

+ Try this:

Given: 0.000567Given: 0.000567

Start with:

Decimal needs to move:

Answer:

+ Change Scientific Notation back to Standard Form Simply move the decimal point to the right for Simply move the decimal point to the right for positive exponent 10. positive exponent 10.

Move the decimal point to the left for negative Move the decimal point to the left for negative exponent 10.exponent 10.

(Use zeros to fill in places.)(Use zeros to fill in places.)

Example:Example:

Given: 5.093 x 10Given: 5.093 x 1066

Move: 6 places to the right (positive)Move: 6 places to the right (positive)

Answer: 5,093,000Answer: 5,093,000

+ Try This:

Given: 1.976 x 10Given: 1.976 x 10-4-4

Move:Move:

Answer: Answer: