Very large or very small numbers are sometimes written in scientific notation. A number written in scientific notation is a decimal number between 1 and 10 multiplied by a power of 10.
Example 1
Express the following in scientific notation.
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2,100,000 written in scientific notation is 2.1 × 10 6. Simply place the decimal point to get a number between 1 and 10 and then count the digits to the right of the decimal to get the power of 10.
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0.0000004 written in scientific notation is 4.0 × 10 –7. Simply place the decimal point to get a number between 1 and 10 and then count the digits from the original decimal point to the new one.
Notice that number values greater than 1 have positive exponents as the power of 10 and that number values between 0 and 1 have negative exponents as the power of 10.
Multiplication in scientific notation
To multiply numbers in scientific notation, multiply the numbers that are between 1 and 10 together to get a whole number. Then add the exponents on the 10's to get a new exponent on 10. It may be necessary to make adjustments to this answer in order to correctly express it in scientific notation.
Example 2
Multiply and express the answers in scientific notation.
This answer must be changed to scientific notation (first number from 1 to 9):
30 × 10 12 = 3.0 × 10 1 × 10 12 = 3.0 × 10 13
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c
Division in scientific notation
To divide numbers in scientific notation, divide the numbers that are between 1 and 10 to get a decimal number. Then subtract the exponents on the 10s to get a new exponent on 10. It may be necessary to make adjustments to this answer in order to correctly express it in scientific notation.
Example 3
Divide and express the answers in scientific notation.
This answer must be changed to scientific notation.
0.4 × 10 2 = 4 × 10 –1 × 10 2 = 4 × 10 1
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e