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Multiplying Numbers In Scientific Notation

To multiply numbers in scientific notation:

Step 1 : Group the numbers together.

Step 2 : Multiply the numbers.

Step 3 : Use the law of indices to simplify the powers of 10.

Step 4 : Give the answer in scientific notation.

Example:

Evaluate 8 × 10³ × 9 × 10², giving your answer in scientific notation.

Solution:

Text Box: 8 × 103 × 9 × 102 = (8 × 9) × 103 × 102 (group the numbers) = 72 × 103 × 102 (multiply the numbers) = 72 × 103+2 (law of indices: am × an = am+ n) = 72 × 105 = 7.2 × 10 × 105 (change to scientific notation) = 7.2 × 106

Example:

Evaluate 12.3 × 0.03, giving your answer in scientific notation.

Solution:

Text Box: 12.3 × 0.03 = 1.23 × 10 × 3 × 10-2 (change to scientific notation) = (1.23 × 3) × 10 × 10-2 (group the numbers) = 3.69 × 10 × 10-2 (multiply the numbers) = 3.69 × 101-2 (law of indices: am × an = am+ n) = 3.69 × 10-1 (already in scientific notation)

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