Scientific Notation

2012-2013

What is scientific Notation?

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

It is most often used in “scientific” calculations where the analysis must be very precise.

Scientific notation consists of two parts:

A number is expressed in scientific notation when it is in the forma x 10n

where a is between 1 and 10and n is an integer

Are these numbers in scientific notation? 2.98393 x 109

4.19385930 x 104/5

9.8920188438 x 10-3

2.22221 x 10000

Yes

No

Yes

No

Powers of Ten When multiplying or dividing by powers of

ten, we can use a shortcut to solve. Multiplying:

1. count the number of zeros2. move decimal point that number of places to the right

Dividing:1. count the number of zeros2. move decimal point that number of places to the left

Exponents of Ten

When powers of ten are expressed as exponents, the exponent represents the number of zeros.

Ex. 105 = 100,000 Ex. 1012 = 1,000,000,000,000

Examples 38 x 102=

2.43 x 107 =

0.00321 x 1,000 =

12 ÷ 10,000=

93.6 ÷ 102 =

3,800

24,300,000

3.21

1,200,000

9,360

Changing standard form to scientific notation.

To change standard form to scientific notation… Place the decimal point so that there is

one non-zero digit to the left of the decimal point.

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

Continued…

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

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

Example 1

Given: 289,800,000. 2.898 Decimal point moved 8 places Original number is greater than 1 Answer: 2.898 x 108

Example 2

Given: 0.000567 5.67 Decimal point moved 4 places Original number is less than 1 Answer: 5.67 x 10-4

Convert to Scientific Notation 0.00264

3,298,034

4

134.62

2.64 x 10-3

3.298034 x 106

4 x 100

1.3462 x 102

Changing scientific notation to standard form.

To change scientific notation to standard form… Simply move the decimal point to the

right for positive exponent of 10. Move the decimal point to the left for

negative exponent of10.

(Use zeros to fill in places.)

Example 3

Given: 5.093 x 106

moved 6 places to the right Fill in extra places with zeros Answer: 5,093,000

Example 4

Given: 1.976 x 10-4

moved 4 places to the left Fill in extra places with zeros Answer: 0.0001976

Convert to standard form 3.256 x 10-2

5.6023 x 104

9. 2 x 108

0.03256

56,023

920,000,000

Using the Calculator In order to enter a number in scientific

notation into the calculator, we use the EE button

Ex. 3.26 x 104

enter the number : 3.26 click the 2nd key click the EE (above the x-1) enter the exponent : 4 click equals

Using the Calculator When a calculation yields a very large

or very small number, some calculators will give the answer in scientific notation.

If the calculator says a EE b– The a is the number– The b is the exponent of ten

Ex. 4.3 EE -7 = 4.3 x 10-7