| Share
 

Scientific Notation

Sometimes, especially when you are using a calculator, you may come up with a very long number. It might be a big number, like 2,890,000,000. Or it might be a small number, like 0.0000073.


Scientific notation is a way to make these numbers easier to work with. In scientific notation, you move the decimal place until you have a number between 1 and 10. Then you add a power of ten that tells how many places you moved the decimal.

In scientific notation, 2,890,000,000 becomes 2.89 x 109. How?

  • Remember that any whole number can be written with a decimal point. For example: 2,890,000,000 = 2,890,000,000.0
  • Now, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the left in 2,890,000,000 you will get 2.89.
  • Next, count how many places you moved the decimal point. You had to move it 9 places to the left to change 2,890,000,000 to 2.89. You can show that you moved it 9 places to the left by noting that the number should be multiplied by 109.
2.89 x 109 = 2.89 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
2.89 x 109 = 2,890,000,000

Scientific notation can be used to turn 0.0000073 into 7.3 x 10-6.

  • First, move the decimal place until you have a number between 1 and 10. If you keep moving the decimal point to the right in 0.0000073 you will get 7.3.
  • Next, count how many places you moved the decimal point. You had to move it 6 places to the right to change 0.0000073 to 7.3. You can show that you moved it 6 places to the right by noting that the number should be multiplied by 10-6.
7.3 x 10-6 = 0.0000073

Remember: in a power of ten, the exponent—the small number above and to the right of the 10—tells which way you moved the decimal point.

  • A power of ten with a positive exponent, such as 105, means the decimal was moved to the left.
  • A power of ten with a negative exponent, such as 10-5, means the decimal was moved to the right.
Powers of Ten
billions
109 = 1,000,000,000
10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000
millions
106 = 1,000,000
10 x 10 x 10 x 10 x 10 x 10 = 1,000,000
hundred thousands
105 = 100,000
10 x 10 x 10 x 10 x 10 = 100,000
ten thousands
104 = 10,000
10 x 10 x 10 x 10 = 10,000
thousands
103 = 1,000
10 x 10 x 10 = 1,000
hundreds
102 = 100
10 x 10 = 100
tens
101 = 10
ones
100 = 1
tenths
10–1 = 1/10
1/10 = 0.1
hundredths
10–2 = 1/102
1/102 = 0.01
thousandths
10–3 = 1/103
1/103 = 0.001
ten thousandths
10–4 = 1/104
1/104 = 0.0001
hundred thousandths
10–5 = 1/105
1/105 = 0.00001
millionths
10–6 = 1/106
1/106 = 0.000001
billionths
10–9 = 1/109
1/109 = 0.000000001

Information Please® Database, © 2007 Pearson Education, Inc. All rights reserved.

Finding Square RootsNumbers and FormulasFactorials

More on Scientific Notation from Infoplease:


Premium Partner Content
HighBeam Research
Documents Images and Maps Reference
(from Newspapers, Magazines, Journals, Newswires, Transcripts and Books)

Research our extensive archive of more than 80 million articles from 6,500 publications.

Additional search results provided by HighBeam Research, LLC. © Copyright 2005. All rights reserved.

24 X 7

Private Tutor

Click Here for Details
24 x 7 Tutor Availability
Unlimited Online Tutoring
1-on-1 Tutoring