Scientific NotationScientific Notation

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In science, we deal with some In science, we deal with some very very LARGELARGE numbers: numbers:

1 mole = 6020000000000000000000001 mole = 602000000000000000000000

In science, we deal with some In science, we deal with some very very SMALLSMALL numbers: numbers:

Mass of an electron =Mass of an electron =0.000000000000000000000000000000091 kg0.000000000000000000000000000000091 kg

Scientific NotationScientific Notation

Imagine the difficulty of Imagine the difficulty of calculating the mass of 1 mole calculating the mass of 1 mole of electrons!of electrons!

0.00000000000000000000000000000000.000000000000000000000000000000091 kg91 kg x 602000000000000000000000x 602000000000000000000000

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Scientific Scientific Notation:Notation:A method of representing A method of representing

very large or very small very large or very small numbers in the form:numbers in the form:

M x 10M x 10nn

MM is a number between is a number between 11 and and 99 nn is an integer equal to is an integer equal to the number of decimal the number of decimal places movedplaces moved

2 500 000 000

Step #1: Insert an understood decimal pointStep #1: Insert an understood decimal point

.

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal point

123456789

Step #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

2.5 x 102.5 x 1099

The exponent is the number of places we moved the decimal.

0.00005790.0000579

Step #2: Decide where the decimal Step #2: Decide where the decimal must end must end up so that one number is to its up so that one number is to its leftleftStep #3: Count how many places you Step #3: Count how many places you bounce bounce the decimal pointthe decimal pointStep #4: Re-write in the form M x 10Step #4: Re-write in the form M x 10nn

1 2 3 4 5

5.79 x 105.79 x 10-5-5

The exponent is negative because the number we started with was less than 1.

PERFORMING PERFORMING CALCULATIONCALCULATION

S IN S IN SCIENTIFIC SCIENTIFIC NOTATIONNOTATION

ADDITION AND ADDITION AND SUBTRACTIONSUBTRACTION

ReviewReview::Scientific notation Scientific notation expresses a number in the expresses a number in the form:form: M x 10M x 10nn

1 1 M M 1010

n is an n is an integerinteger

4 x 104 x 1066

+ 3 x 10+ 3 x 1066

IFIF the exponents the exponents are the same, we are the same, we simply add or simply add or subtract the subtract the numbers in front numbers in front and bring the and bring the exponent down exponent down unchanged.unchanged.

77 x 10x 1066

4 x 104 x 1066

+ 3 x 10+ 3 x 1055

If the exponents If the exponents are NOT the are NOT the same, we must same, we must move a decimal to move a decimal to makemake them the them the same.same.

4.00 x 104.00 x 1066

+ + 3.00 x 103.00 x 1055 + + .30 x 10.30 x 1066

4.304.30 x 10x 1066

Move the Move the decimal decimal on the on the smallersmaller number!number!

4.00 x 104.00 x 1066

A Problem for A Problem for you…you…

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

2.37 x 102.37 x 10-6-6

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…002.37 x 10002.37 x 10--

66

+ 3.48 x 10+ 3.48 x 10-4-4

Solution…Solution…0.0237 x 100.0237 x 10-4-4

3.5037 x 103.5037 x 10-4-4

Scientific Notation and your Scientific Notation and your calculatorcalculator

To enter a number in scientific notation on your calculator follow these steps:

#1 Type in the decimal number- ex 6.022

#2 For most TI calculators press 2nd and then the EE button (usually above the x2 or x-1 buttons)

- This represents x 10n in calculator language

DO NOT TYPE IN x 10^n YOU WILL GET THE WRONG ANSWER!

List the value of the List the value of the following exponential termsfollowing exponential terms

__________ 1) 1.0 x 103

 __________ 2) 1.0 x 100

 __________ 5) 1.0 x 10-3

Put the following numbers Put the following numbers into scientific notation.into scientific notation.

__________ 6) 588.762 __________ 7) 0.00000722 __________ 8) 4,310,000 __________ 9) 0.004100

Take the following numbers Take the following numbers out of scientific notationout of scientific notation

____________________ 10) 3.67 x 105

 ____________________ 11) 2.099 x 103

 ____________________ 12) 3.1 x 10-1

 ____________________ 13) 5.04 x 10-5

 ____________________ 14) 2.00 x 100

Put the following numbers Put the following numbers into correct scientific into correct scientific notation f sig figs indicatednotation f sig figs indicated

________ 15) 30,000 (3 sig figs) ________ 16) 115,000,000 (2 sig figs) ________ 17) 106,000 (4 sig figs) ________ 18) 0.0412 (3 sig figs) ________ 19) 0.0233006 (2 sig figs) ________ 20) 0.00149999999 (3 sig figs)

Solve the following problems. Put the Solve the following problems. Put the answers into correct scientific notation answers into correct scientific notation form. (Yes, sig figs matter.)form. (Yes, sig figs matter.)

________ 21) 1.50 x 102 / 2.39 x 10-1

 ________ 22) 3.29 x 105 / 2.1 x 106

 ________ 23) 1.50 x 104 * 2.3 x 10-3

 ________ 24) 8.000 x 10-3 * 2.67 x 101

 ________ 25) 2.60 x 106 * 1.50 x 10-2