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:

Multiply (3 x 10³)(5 x 10^-2)

Solution:

Division

Follow the steps listed below when dividing numbers in scientific notation.

Step 1:Divide one decimal into the other.

Step 2:Divide one power of ten into the other by subtracting the exponents.

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

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

Example:

Solution:

Summary

Pertinent information concerning scientific notation is summarized below.

Scientific Notation Summary

When changing from integer form to scientific notation:

If the decimal is shifted left, the exponent is positive.

If the decimal is shifted right, the exponent is negative.

When adding or subtracting numbers in scientific notation, change both numbers to the same power of ten by moving the decimal point. Add or subtract the decimal numbers, and keep the power of ten. Rewrite if necessary.

To multiply two numbers in scientific notation, multiply decimal numbers and add exponents. Rewrite if necessary.

To divide two numbers in scientific notation, divide decimal numbers and subtract exponents. Rewrite if necessary.