Scientific Notation
A method for expressing a given quantity as a number having the significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power.
Scientific notation is helpful in writing very large or very small numbers with few significant digits.
.

A number	written in Scientific Notation
	has two parts:
Example:
. 2,400	the Coefficient the power of ten . 2.4 x 103 . The decimal moved 3 places to the left.
	.
	In the coefficient, In the power of ten, there is one number— between 1 & 9— to the left of a decimal. No zeros ever go to the left of the decimal. The only time zeros go to the right of the decimal are when they are between numbers or the zeros came at the end of a decimal number. if the number is greater than one, then the exponent is positive—and the decimal will move that number to the left.  <— If the number is less than one, then the exponent is negative—and the decimal will move that number to the right.  —>   .
.
Example:
. 0.018	the Coefficient the power of ten . 1.8 x 10-2 . The decimal moved 2 places to the right.
.

.
Powers of Ten
 

Number	Multiples of Ten	Scientific Notation
1,000	10 x 10 x 10	103
100	10 x 10	102
10	10	10 or 101
1	0	100
0 .1	1/10	10-1
0 .01	1/10 x 1/10	10-2
0 .001	1/10 x 1/10 x 1/10	10-3

.
Example:

To write the measurement 23,000 °C in scientific notation, move the decimal from the end of the number to right after the 2 — that is 4 spaces to the LEFT.

That gives you a coefficient of 2.3

For the power of ten, since the decimal was moved 4 spaces to the left, the exponent on the power of ten is a 4.

Therefore, 23,000 °C = 2.3 x 10⁴ °C

What is Scientific Notation?
 

Practice Problems Answer the following questions:

1. What are the two parts of a number written in scientific notation?

2. Restate the following measurements in scientific notation: . a) 350 g b) 0.000 16 L c) 5,220,000 m . d) 425,000 K e) 0.000 000 8 s g) 3,050 g/mL

3. Restate the following measurements in scientific notation: . a) 4.9 x 10-4 s b) 5.5 x 104 °C c) 3.25 x 102 g . d) 6 x 106 m e) 7 x 10-5 m f) 1.2 x 10-3 g

4. Can a zero ever go to the left of the decimal in the coefficient of a number written in scientific notation? Can a zero ever go to the right of the decimal in the coefficient of a number written in scientific notation?

5. If the original measurement is ten thousand kelvin, which direction will the decimal move, and what will be the exponent in the power of ten?  Is the exponent positive or negative?

6. If the original measurement is one thousandth of a meter, which direction will the decimal move, and what will be the exponent in the power of ten?  Is the exponent positive or negative?