# Using Scientific Notation

Updated February 21, 2017 | Factmonster Staff 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 billions109 = 1,000,000,00010 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000,000 millions106 = 1,000,00010 x 10 x 10 x 10 x 10 x 10 = 1,000,000 hundred thousands105 = 100,00010 x 10 x 10 x 10 x 10 = 100,000 ten thousands104 = 10,00010 x 10 x 10 x 10 = 10,000 thousands103 = 1,00010 x 10 x 10 = 1,000 hundreds102 = 10010 x 10 = 100 tens101 = 10 ones100 = 1 tenths10?1 = 1/101/10 = 0.1 hundredths10?2 = 1/1021/102 = 0.01 thousandths10?3 = 1/1031/103 = 0.001 ten thousandths10?4 = 1/1041/104 = 0.0001 hundred thousandths10?5 = 1/1051/105 = 0.00001 millionths10?6 = 1/1061/106 = 0.000001 billionths10?9 = 1/1091/109 = 0.000000001