Scientific Notation

So you don’t have to write so many zeros…Yay!

Standard vs, Scientific

• Standard Notation: no exponents:– Ex. 102,000 0.00045 1,000,000,000

• Scientific Notation: has exponents:– Ex. 2.3x10-4 5.6x103 6.022x1023

Of Course There Are Rules!

1. A positive exponent represents a number bigger than 1.

Ex. 3.8x104 = 38,000

4x102 = 400

Of Course There Are Rules!

2. A negative exponent represents a number smaller than 1.

Ex. 9.2x10-3 = 0.0092

4x10-2 = 0.04

Of Course There Are Rules!

3. An exponent of 0 does not change the number because 100=1:

Ex. 2.3x100 = 2.3 x 1 = 2.3

1.6x100 = 1.6

5.8x100 = 5.8

From Standard to Scientific

1. Place a decimal where there would be ONE real number in front.

2. Count how many places you had to move it over. This is your exponent.

3. If the original number is smaller than 1, put a negative in your exponent.

From Scientific to Standard

1. If the exponent is negative, move the decimal left to make the number smaller than one.

The number of times you move it = the exponent.

2. If the exponent is positive, move the decimal right to make the number bigger than one.

The number of times you move it = the exponent.

Since We’re At It…

• SI = Système Internationale

• Universal units of measurement for science.

• Based on 10, so there are exponents everywhere.

• You’ll need these for next time, so don’t lose your paper!!

SI Prefixes!!

Symbol Prefix Scientific Standard

M Mega 106 1,000,000

k kilo 103 1,000

‘base unit’ = meter, liter, gram, second = 100 = 1

d deci 10-1 0.1

c centi 10-2 0.01

m milli 10-3 0.001

u micro 10-6 0.000001

n nano 10-9 0.000000001

Let’s Practice!

• Worksheet for you!! (Get used to it.)

• Do the front only! We’ll do the back at the end of class.

Significant Figures

More Stuff to Memorize!

Why We Need Significant Figures• Any measurement has uncertainty.

• Significant figures tell us which digit is estimated. (usually the last number)

Rule #1

• Any number that is not a zero is significant. No matter what.

• 34.5 has how many significant figures? 3

Rule #2

• Zeros that come before the non-zero numbers are never significant.– These are called “leading zeros.”

• 0.0054 has how many significant figures? 2

Rule #3

• Zeros that are between the non-zero numbers are always significant.– These are called “captive zeros.”

• 1.002 has how may significant figures? 4

Rule #4

• Zeros at the end of a number are only significant if there is a decimal point in your number.– These are called “trailing zeros.”

• 1000 has how many significant figures?

• 1000. has how many significant figures?

• 3.40 x 104 has how many significant figures?

14

3

RoundingDo all calculations before you round.

1. Figure out how many sig figs you need.

2. Find the number right after the last sig fig you need.

3. If that number is less than 5, the digit before stays the same.

4. If that number is five or more, the last sig fig goes up by one number.

5. Any extra numbers on the end just go away.

Ex: Round 3.4048 to three significant figures.

3.40

Addition and Subtraction

• The answer has as many significant figures as the term with the smallest number of decimal places.

• 12.11+18.0+1.013=?

• How many decimal places should your answer have? 1

31.123 31.1

Multiplication and Division

• The answer has the same amount of significant figures as the term with the smallest number of significant figures.

• 4.56 x 1.4 = ?

• How many significant figures does your answer need?

6.384 6.4

2

More Practice!

• Finish the back of your worksheet!

• Turn it into the purple crate when you’re done and move your fish!