Scientific Notation

Basics

• All numbers written in scientific notation will look like this:

n x 10a

n = a number that is greater than or equal to one and less than 10 1 ≤ n < 10

a = the number of times the decimal moved when the

number was in standard form. The number in standard form determines whether the exponent is positive or negative.

Positive Exponent

• The exponent will be positive if the number in standard form is greater than 1.

• Example: 549.3 This is a number greater than 1. To write this in scientific notation, move the decimal point two (2) times to the left to make a number less than 10 but greater than or equal to 1.

5.493 5.493 X 102

Now the power of 10 that goes with this number will have a positive exponent of 2 because we moved the decimal two times and the number was greater than 1 in standard form.

Negative Exponent

• The exponent will be negative if the number in standard form is less than 1.

• Example: .000298 This is a number that is less than 1. To write this in scientific notation move the decimal four (4) times to the right in order to get a number less than 10 and greater than or equal to 1.

2.98 2.98 x 10-4

The power of 10 that goes with this number will have a negative exponent because the number in standard form was less than 1.

Practice Problems

• Write the following numbers in scientific notation.

1. 12.9 2. 999 3. .000007

4. .056 5. 18 6. .000288

• Write the following numbers back in standard form.

1. 4.3 x 10-3 2. 9.825 x 102 3. 5.04 x 10-1

4. 1.0001 x 105 5. 3.77 x 10-4 6. 8.1 x 103