Scientific Notation Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scientific Notation Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Performing addition, subtraction, multiplication, and division on numbers expressed in scientific notation.

Multiplying and dividing are straightforward: multiply or divide the coefficients and add or subtract the exponents. Adding and subtracting require matching the powers of 10 first, like finding a common denominator.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Multiplication and division work with exponent rules directly; addition and subtraction require the same power of 10 first.

Common stuck point: Adding or subtracting numbers with different exponents requires rewriting one number so both have the same power of 10 before combining coefficients.

Sense of Study hint: Before adding or subtracting, rewrite both numbers so they have the same power of 10, then combine only the coefficients.

Worked Examples

Example 1

medium
Compute (3.2 \times 10^5) \times (4.0 \times 10^{-3}) and express in scientific notation.

Solution

  1. 1
    Multiply the coefficients: 3.2 \times 4.0 = 12.8.
  2. 2
    Multiply the powers of 10: 10^5 \times 10^{-3} = 10^{5+(-3)} = 10^2.
  3. 3
    Combine: 12.8 \times 10^2.
  4. 4
    Adjust to proper scientific notation (coefficient must satisfy 1 \leq c < 10): 12.8 = 1.28 \times 10^1, so 12.8 \times 10^2 = 1.28 \times 10^3.

Answer

1.28 \times 10^3
To multiply in scientific notation: multiply the coefficients, add the exponents (using 10^a \times 10^b = 10^{a+b}), then adjust so the coefficient is between 1 and 10. This mirrors the exponent rules for powers of the same base.

Example 2

hard
Compute \dfrac{6.0 \times 10^8}{2.4 \times 10^{-2}} and (5.0 \times 10^3) + (3.0 \times 10^2), expressing both in scientific notation.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Compute (2.5 \times 10^4) \times (3.0 \times 10^6). Express your answer in scientific notation.

Example 2

medium
The mass of the Earth is 5.97 \times 10^{24} kg. The mass of the Moon is 7.35 \times 10^{22} kg. How many times heavier is the Earth than the Moon?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

scientific notationexponent rules