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§ 9.5. Scientific Notation. greater than 1 and less than 10. a power of 10. Scientific notation. Scientific Notation. A positive number is in scientific notation if it is in the form a  10 n , where a is a number greater than (or equal to) 1 and less than 10, and n is an integer.

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§ 9.5

Scientific Notation


Scientific notation

greater than 1 and less than 10

a power of 10

Scientific notation

Scientific Notation

A positive number is in scientific notation if it is in the form a 10n, where a is a number greater than (or equal to) 1 and less than 10, and n is an integer.

5600 = 5.6  1000 = 5.6  103

78,200,000 = 7.82  10000000 = 7.82  107


Standard notation to scientific notation

What power?

Ending position of decimal point

Starting position of decimal point

Standard Notation to Scientific Notation

Example: Write 67,300 in scientific notation.

67,300. = 6.73  10

The decimal point was moved 4 places to the left, so we use a power of 4.

67,300 = 6.73  104

A number that is larger than 10 and written in scientific notation will always have a positive exponent as the power of 10.


Negative exponents

The positive exponent indicates the number of places to move the decimal place to the right.

Any number to the zero power is 1.

The negative exponent indicates the number of places to move the decimal place to the left.

Negative Exponents

Notice the following pattern when raising a base of 10 to positive and negative exponents.


Standard notation to scientific notation1

What power? the decimal place to the right.

Ending position of decimal point

Starting position of decimal point

Standard Notation to Scientific Notation

Example: Write 0.048 in scientific notation.

0.048 = 4.8  10

The decimal point was moved 2 places to the right, so we use a power of –2.

0.048 = 4.8  10–2

A number that is smaller than 1 and written in scientific notation will always have a negative exponent as the power of 10.


Scientific notation to standard notation
Scientific Notation to Standard Notation the decimal place to the right.

Example: Write 9.1  104 in standard notation.

9.1  104

= 9.1000  104

= 91,000

Move the decimal point 4 places to the right.

Example: Write 6.72  10–3 in standard notation.

6.72  10–3

= 6.72  10–3

= 0.00672

Move the decimal point 3 places to the left.


Adding and subtracting in scientific notation

4.52 the decimal place to the right.  108

Add the decimal part.

Leave the power of 10 unchanged.

+ 5.63  108

0.842  105

Rewrite 8.42  104 as 0.842 105.

– 1.78  105

Adding and Subtracting in Scientific Notation

Numbers in scientific notation may be added or subtracted if they have the same power of 10. We add or subtract the decimal part and leave the power of 10 unchanged.

Example: Add. 4.52  108 + 5.63  108

10.15  108

Example: Subtract. 8.42  104– 1.78  105

10.15  105


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