Scientific Notation

4 minQuiz at the end

What is Scientific Notation?

Scientific notation (also called standard form) is a way of writing very large or very small numbers using powers of 10.

Format: a Γ— 10ⁿ, where 1 ≀ a < 10 and n is an integer.

Writing Large Numbers

Move the decimal point left until you have a number between 1 and 10. The number of places moved = the exponent.

3,500,000 β†’ move decimal 6 places left β†’ 3.5 Γ— 10⁢

Writing Small Numbers

Move the decimal point right until you have a number between 1 and 10. Use a negative exponent.

0.000042 β†’ move decimal 5 places right β†’ 4.2 Γ— 10⁻⁡

Converting Back to Standard Form

Positive exponent β†’ move decimal right:

  • 6.02 Γ— 10Β³ = 6,020

Negative exponent β†’ move decimal left:

  • 5.1 Γ— 10⁻³ = 0.0051

Why Use Scientific Notation?

Without it, we'd write numbers like:

  • The distance to the nearest star: 40,208,000,000,000 km vs 4.02 Γ— 10ΒΉΒ³ km
  • The mass of a proton: 0.000000000000000000000000001673 kg vs 1.673 Γ— 10⁻²⁷ kg

Comparing Numbers in Scientific Notation

Compare the exponents first. If equal, compare the a values.

  • 4.2 Γ— 10⁡ vs 8.1 Γ— 10⁴ β†’ 10⁡ > 10⁴, so 4.2 Γ— 10⁡ is larger