Multiplication: Using Scientific Notation

When multiplying two or more numbers in scientific notation, the following steps must be used.

Step 1: Multiply the decimal numbers and obtain the product.

Step 2: Multiply the powers of ten together by adding the exponents.

Step 3: Put the product in single-digit scientific notation.

Step 4: If necessary, rewrite decimal with a single number to the left of the decimal point.

Example 1:

Multiply (3 x 103)(5 x 10-2)

Solution:

Step 1: 3 x 5 = 15

Step 2: 103 x 10-2 = 103+-2 =101

Step 3: The product is: 15 x 101

Step 4: = 1.5 x 102

The answer is1.5 x 102

Example 2

Multiply:(4 x 104)(3 x 10-2 = ?

Solution

Step 1: Multiply the decimal numbers and obtain the product.

4 x 3 = 12

Step 2: Multiply the powers of ten together by adding the exponents.

(104)(10-2)= 104+-2 = 102

Step 3: Put the product in single-digit scientific notation.

12 x 102

Step 4: If necessary, rewrite decimal with a single number to the left of the decimal

point.

1.2 x 103

The answer is: 1.2 x 103

Example 3

Multiply (3 x 104)(8 x 103)

Solution

Step 1: Multiply the decimal numbers and obtain the product.

3 x 8 = 24

Step 2: Multiply the powers of ten together by adding the exponents.

104)(8 x 103) = 104+3 = 107

Step 3: Put the product in single-digit scientific notation.

24 x 107Step 4: If necessary, rewrite decimal with a single number to the left of the

decimal point.

2.4 x 108

The answer is 2.4 x 108