Subtraction: Using Scientific Notation

In order to subtract two numbers in scientific notation, the steps listed below must be followed.

Step 1: As in addition, change all addends to have the same power of ten.

Step 2: Subtract one digit from the other and keep the power of ten.

Step 3: If necessary, rewrite the decimal with a single number to the left of the decimal point.

Example:

Subtract (3.27 x 104) - (2 x 103)

Solution:

Step 1: (3.27 x 104) = (3.27 x 104)

2.00 x 103 = 0.20 x 104

Step 2: (3.27 x 104) - (0.20 x 104)

Step 3: 3.07 x 104

The answer is 3.07 x 104

Example

Subtract: (6.35 x 105) - (21 x 104)

Solution

Step 1: As in addition, change all addends to have the same power of ten.

(6.35 x 105)= (6.35 x 105)

(21 x 104)= (2.1 x 105)

Step 2: Subtract one digit from the other and keep the power of ten.

(6.35 x 105)- (2.1 x 105) =

Step 3: If necessary, rewrite the decimal with a single number to the left of the decimal point.

4.25 x 105

The answer is:4.25 x 105

Example

Subtract: (8.12 x 104)-(6 x 103)

Step 2: Subtract one digit from the other and keep the power of ten.

(8.12 x 104)= (8.12 x 104)

(6 x 103)= .60 x 104

Step 3: If necessary, rewrite the decimal with a single number to the left of the decimal point.

(8.12 x 104)- (.60 x 104)= 7.52 x 104.

Therefore, the answer is 7.52 x 104