CMClearMathAcademy

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.

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.

Answer: 5.2 x 10^4

Practice problems

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: Write 4,000 as a power of 10 expression.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 4,000 is 4 times 1,000.
  4. 1,000 is 10^3.
  5. Check the result by substituting or estimating: the response should match 4 x 10^3 and make sense in the original problem.

Answer: 4 x 10^3

2. Write 35,000 in scientific notation.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Write 35,000 in scientific notation.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Move the decimal after 3.
  4. The decimal moved 4 places left.
  5. Check the result by substituting or estimating: the response should match 3.5 x 10^4 and make sense in the original problem.

Answer: 3.5 x 10^4

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

Show solution
  1. Warm-up: First identify exactly what the question is asking: Write 6.2 x 10^3 in standard form.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 10^3 means move the decimal 3 places right.
  4. 6.2 becomes 6200.
  5. Check the result by substituting or estimating: the response should match 6200 and make sense in the original problem.

Answer: 6200

4. Write 780,000 in scientific notation.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Write 780,000 in scientific notation.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Move the decimal after 7.
  4. The decimal moved 5 places left.
  5. Check the result by substituting or estimating: the response should match 7.8 x 10^5 and make sense in the original problem.

Answer: 7.8 x 10^5

5. Write 0.0045 in scientific notation.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Write 0.0045 in scientific notation.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Move the decimal to make 4.5.
  4. The decimal moved 3 places right, so the exponent is -3.
  5. Check the result by substituting or estimating: the response should match 4.5 x 10^-3 and make sense in the original problem.

Answer: 4.5 x 10^-3

Practice this interactively with instant feedback and an AI tutor.

Practice Scientific Notation Take the free placement check

More Pre-Algebra lessons