ObjectiveThe student will be able to:

express numbers in scientific and decimal notation.

How wide is our universe?

210,000,000,000,000,000,000,000 miles(22 zeros)

This number is written in decimal notation. When numbers get this large, it is easier to write them in

scientific notation.

Scientific Notation

A number is expressed in scientific notation when it is in the form

a x 10n

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

Write the width of the universe in scientific notation.

210,000,000,000,000,000,000,000 milesWhere is the decimal point now?

After the last zero.Where would you put the decimal to make

this number be between 1 and 10?Between the 2 and the 1

2.10,000,000,000,000,000,000,000.

How many decimal places did you move the decimal?

23When the original number is more than 1,

the exponent is positive.The answer in scientific notation is

2.1 x 1023

1) Express 0.0000000902 in scientific notation.

Where would the decimal go to make the number be between 1 and 10?

9.02The decimal was moved how many places?

8When the original number is less than 1, the

exponent is negative.9.02 x 10-8

Write 28750.9 in scientific notation.

1. 2.87509 x 10-5

2. 2.87509 x 10-4

3. 2.87509 x 104

4. 2.87509 x 105

2) Express 1.8 x 10-4 in decimal notation.

0.000183) Express 4.58 x 106 in decimal notation.

4,580,000On the graphing calculator, scientific notation is done with the button.

4.58 x 106 is typed 4.58 6

Write in PROPER scientific notation.(Notice the number is not between 1 and 10)

8) 234.6 x 109

2.346 x 1011

9) 0.0642 x 104

on calculator: 6426.42 x 10 2

Write 531.42 x 105 in scientific notation.

1. .53142 x 102

2. 5.3142 x 103

3. 53.142 x 104

4. 531.42 x 105

5. 53.142 x 106

6. 5.3142 x 107

7. .53142 x 108

Scientific Notation

Quick Review

Powers of 10

• http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/

• http://www.powersof10.com/

• Powers of 10 - Google Videos

Question 1Write 4,776 in scientific notation

Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between

one and ten.

4.776Count the number of digits between the old and the new

decimal point, this gives the power, n of 10 (10n).

4 776 X 103

Since the decimal is shifted to the left, the exponent is positive.

4.776 x 103

3 Digits

Question 6Write 0.0246 in scientific notation

Place the decimal immediately to the right of the left-most non-zero number. This should give you a number between one

and ten

2.46Count the number of digits between the old and the new

decimal point, this gives the power, n of 10 (10n).

X 10-2

Since the decimal is shifted to the right, the exponent is negative.

2.46 x 10-2

2 Digits

0 02 46

Question 14Write 4.953 x 104 in standard form

Write the decimal number.

4.953Move the decimal the number of places specified by the powers of ten: to the right since it is positive.

X 104 4 9530Rewrite the number in integer/standard form.

49,530

4 Places

Question 17Write 8.397 x 10-1 in standard form

Write the decimal number.

8.397Move the decimal the number of places specified by

the powers of ten: to the left since it is negative.

X 10-1 0 8 397Rewrite the number in integer/standard form.

0.8397

1 Place

Multiplying and Dividing With Your Calculator

1. Punch the number (the digit number) into your calculator.

2. Push the EE or EXP button. Do NOT use the x (times) button!!

3. Enter the exponent number. Use the +/- button to change its sign.

4. Voila! Treat this number normally in all subsequent calculations.

• Scientific Calculator• Scientific calculator for chemists with notebook• http://www.calculator.com/calcs/calc_sci.html

Scientific Notation Tutorials

• http://www.wwnorton.com/college/chemistry/gilbert/tutorials/ch1.htm

(Click on Scientific Notation Link - view tutorial)

• http://www.visionlearning.com/library/

module_viewer.php?mid=47&l=&c3 (Read Scientific Notation towards the bottom of the page)

• http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut3_scinot.htm