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Scientific Notation

A free Pre-Algebra lesson from the “Decimals, Roots, and the Real Number System” unit, with a worked example and practice problems including step-by-step solutions.

Scientific notation writes numbers as a number from 1 up to 10 multiplied by a power of 10. Positive exponents make large numbers, and negative exponents make small decimals. In Decimals, Roots, and the Real Number System, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

Why it matters: Distances to planets, the size of a virus, and population figures are written in scientific notation. The form keeps very large and very small numbers compact and easy to compare.

Worked example

Problem. Write 52,000 in scientific notation.

  1. Move the decimal so the first factor is between 1 and 10: 5.2.
  2. The decimal moved 4 places left.
  3. So 52,000 = 5.2 x 10^4.
  4. Connect the calculation back to Scientific Notation so the method, not just the arithmetic, is clear.

Answer: 5.2 x 10^4

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.

Practice problems

1. Write 4,000 as a power of 10 expression.

Show solution
  1. 4,000 is 4 times 1,000.
  2. 1,000 is 10^3.

Answer: 4 x 10^3

2. Write 35,000 in scientific notation.

Show solution
  1. Move the decimal after 3.
  2. The decimal moved 4 places left.

Answer: 3.5 x 10^4

3. Write 6.2 x 10^3 in standard form.

Show solution
  1. 10^3 means move the decimal 3 places right.
  2. 6.2 becomes 6200.

Answer: 6200

4. Write 780,000 in scientific notation.

Show solution
  1. Move the decimal after 7.
  2. The decimal moved 5 places left.

Answer: 7.8 x 10^5

5. Write 0.0045 in scientific notation.

Show solution
  1. Move the decimal to make 4.5.
  2. The decimal moved 3 places right, so the exponent is -3.

Answer: 4.5 x 10^-3

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