Metric System

Question of the Day Question: How much is a ‘kilodollar’ worth and how do you know? Answer: … … …

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

It makes using very large and very small numbers easier! 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 Exponent Number between 1 and 10 (not including 10)

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

149597870700. The distance to the Sun is 149,597,870,700. meters How do we write that in Scientific Notation? Write the number down leaving out commas but show the decimal point 149597870700.

The distance to the Sun is 149,597,870,700. meters Write the number down leaving out commas but show the decimal point 149597870700. 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 Write the number down leaving out commas but show the decimal point 149597870700. 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 Write the number down leaving out commas but show the decimal point 149597870700. 11 spaces 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 11 spaces to the left 1.495978707 x 1011 m Move the decimal point until there is one digit to the left of it, counting the spaces as you go # of spaces = the exponent

0.000000000182 The diameter of a Carbon nucleus is 0.000000000182 meters How do we write that in Scientific Notation? 0.000000000182 10 spaces

0.000000000182 The diameter of a Carbon nucleus is 0.000000000182 meters How do we write that in Scientific Notation? 0.000000000182 10 spaces if you move to the right, put a minus sign in front of the exponent

The diameter of a Carbon nucleus is 0.000000000182 meters 10 spaces to the right 1.82 x 10-10 m if you move the decimal to the right, put a minus sign in front of the exponent

1.495978707 x 1011 m Converting from Scientific Notation to Standard move the decimal point to the right for a positive exponent  to the left for a negative exponent

Converting from Scientific Notation to Standard

Converting from Scientific Notation to Standard 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 Write the Following in Scientific Notation 17 78,942 0.0042

17 78,942 0.0042 1.7 x 101 Let’s Do Some Examples Write the Following in Scientific Notation 17 78,942 0.0042 1.7 x 101

17 78,942 0.0042 1.7 x 101 7.8942 x 104 Let’s Do Some Examples Write the Following in Scientific Notation 17 78,942 0.0042 1.7 x 101 7.8942 x 104

Let’s Do Some Examples Write the Following in Scientific Notation 17 78,942 0.0042 1.7 x 101 4.2 x 10-3 7.8942 x 104

1.7 x 104 1.7 x 10-4 Let’s Do Some Examples Write the Following in Standard (or Long) Form 1.7 x 104 1.7 x 10-4

1.7 x 104 1.7 x 10-4 17000 Let’s Do Some Examples Write the Following in Standard (or Long) Form 1.7 x 104 1.7 x 10-4 17000

1.7 x 104 1.7 x 10-4 17000 0.00017 Let’s Do Some Examples Write the Following in Standard (or Long) Form 1.7 x 104 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