# 15.1: Scientific Notation

- Page ID
- 16048

Scientific notation is a concise method of expressing numbers that are too large or too small to be conveniently represented as decimals. Since science is often concerned with very large things (e.g., galaxies, light years, planets) and very small things (atoms, bacteria, viruses), scientific notation is commonly used in science and engineering.

In scientific notation, all numbers are written in the following form:

**A x 10 ^{n} (A times 10 raised to the power of n)**

“A” represents the digits in the number and “n” is the exponent (or power) to which ten is raised.

Numbers both larger and smaller than one can be represented in scientific notation. If the number is larger than one, the exponent will have a positive value, and if the number is smaller than one, the exponent will have a negative value. For example:

(a) The number 100 can also be written as 1 x 10^{2} (or: 1 times 100 = 100). Scientific notation tells you that you take the number 1, and move the decimal point 2 places to the right of the number.

(b) The number 0.01 can also be written as 1 x 10^{-2} . Scientific notation tells you that you take the number 1 and move the decimal 2 places to the left of the number.

**Some examples:**

a. 223 = 2.23 x 10^{2}

b. 0.000156 = 1.56 x 10^{-4}

c. 7,650,000 = 7.65 x 10^{6}

d. 0.00382 = 3.82 x 10^{-3 }

**Exercises **

Below are a series of exercises that will help familiarize you with scientific notation. 1. Convert the following fractions to their decimal form and their scientific notation form.

1. Convert the following fractions to their decimal form and their scientific notation form.

Fraction | Decimal | Scientific notation |

1/10 | ||

1/100 | ||

1/1000 | ||

1/10000 | ||

1/100000 |

2. Write the following numbers in scientific notation:

a. 4,500 ______________________________

b. 2,220,000 __________________________

c. 0.0035 _____________________________

d. 0.7 ________________________________

e. 858.67 ______________________________

3. The following numbers are written using scientific notation. Convert them to their decimal form.

a. 5.65x 10^{-3} ________________________

b. 9.25 x 10^{-4}_______________________

c. 5.68 x 10^{5} ________________________

d. 1.632 x 10^{3} _______________________

e. 4.8932 x 10^{-2} ______________________