Metric System

Question: How much is a ‘kilodollar’ worth and how do you know?

Answer: … … …

Question of the Day

The Dollar Bill as the Standard Unit

Multiply by 10 and you get a…

dekadollar

Multiply the dollar by 100 and get…

hectodollar

Multiply the dollar by one thousand and you get…

kilodollar

Multiply the dollar by 1 million and you get…

megadollar

Let’s go the other way.We start off with the dollar

again….

Now divide by 10…

Decidollar

Divide the dollar by 100 and you get a…

centidollar

If you were to go further and divide that dollar by 1000, you

would get a…

millidollar

Scientific Notation

It makes using very large and very small numbers easier!

A number in Scientific Notation has two parts

A number in Scientific Notation has two parts

9.9 x 106

A number in Scientific Notation has two parts

9.9 x 106

Number between 1 and 10(not including 10)

A number in Scientific Notation has two parts

9.9 x 106

Number between 1 and 10(not including 10)

Exponent

The distance to the Sun is 149,597,870,700. metersHow do we write that in Scientific Notation?

The distance to the Sun is 149,597,870,700. metersHow do we write that in Scientific Notation?

149597870700.

Write the number down leaving out commas but show the decimal point

The distance to the Sun is 149,597,870,700. meters

149597870700.

Write the number down leaving out commas but show the decimal point

Move the decimal point until there is one digit to the left of it, counting the spaces as you go

The distance to the Sun is 149,597,870,700. meters

149597870700.

Write the number down leaving out commas but show the decimal point

Move the decimal point until there is one digit to the left of it, counting the spaces as you go

The distance to the Sun is 149,597,870,700. meters

149597870700.

Write the number down leaving out commas but show the decimal point

Move the decimal point until there is one digit to the left of it, counting the spaces as you go

11 spaces

The distance to the Sun is 149,597,870,700. meters

1.495978707 x 1011 m

# of spaces = the exponent

11 spaces to the left

Move the decimal point until there is one digit to the left of it, counting the spaces as you go

The diameter of a Carbon nucleus is0.000000000182 meters

How do we write that in Scientific Notation?

0.00000000018210 spaces

The diameter of a Carbon nucleus is0.000000000182 meters

How do we write that in Scientific Notation?

0.00000000018210 spaces

if you move to the right, put a minus sign in front of the exponent

The diameter of a Carbon nucleus is0.000000000182 meters

1.82 x 10-10 m

if you move the decimal to the right, put a minus sign in front of the exponent

10 spaces to the right

Converting from Scientific Notation to Standard

1.495978707 x 1011 m

move the decimal point to the right for a positive exponent to the left for a negative exponent

Converting from Scientific Notation to Standard

149597870700. m

Converting from Scientific Notation to Standard

1.49597870700. m

1.82 x 10-10 m

To convert from Scientific Notation back to Standard, just move the decimal point back, moving to the right for a positive power of 10, to the left for a negative power of 10

149597870700. m

0.000000000182 m

Let’s Do Some Examples

17 78,942

Write the Following in Scientific Notation

0.0042

Let’s Do Some Examples

17 78,942

Write the Following in Scientific Notation

0.0042

1.7 x 101

Let’s Do Some Examples

17 78,942

Write the Following in Scientific Notation

0.0042

1.7 x 101

7.8942 x 104

Let’s Do Some Examples

17 78,942

Write the Following in Scientific Notation

0.0042

1.7 x 101

7.8942 x 104

4.2 x 10-3

Let’s Do Some Examples

1.7 x 104

Write the Following in Standard (or Long) Form

1.7 x 10-4

Let’s Do Some Examples

1.7 x 104

Write the Following in Standard (or Long) Form

1.7 x 10-4

17000

Let’s Do Some Examples

1.7 x 104

Write the Following in Standard (or Long) Form

1.7 x 10-4

17000 0.00017

Multiplying and Dividing numbers in Scientific Notation is Easier

Multiplying and Dividing numbers in Scientific Notation is Easier

To multiply, just multiply the numbers together, then add the exponents

(1.7 x 104) x (2.0 x 108)

= (1.7 x 2.0) x (10(4+8))

= 3.4 x 1012

Multiplying and Dividing numbers in Scientific Notation is Easier

To divide, just divide the numbers then subtract the exponents

(1.0 x 106) ÷ (2.0 x 101)

= (1.0 ÷ 2.0) x (10(6-1))

= 0.5 x 105 = 5.0 x 104