Standard Form Calculator

Convert numbers between standard form, scientific notation, and expanded form

Convert Number Forms

Enter any decimal number, including scientific notation

Common Examples

Very Large Numbers

Mass of Earth
5,972,000,000,000,000,000,000,000 kg
= 5.972 x 10²⁴ kg
Distance to Sun
149,600,000,000 m
= 1.496 x 10¹¹ m

Very Small Numbers

Mass of Electron
0.000000000000000000000000000000911 kg
= 9.11 x 10⁻³¹ kg
Size of Atom
0.0000000001 m
= 1.0 x 10⁻¹⁰ m

Standard Form Rules

Format: a x 10ⁿ

Where 1 ≤ a < 10 and n is an integer

Positive Exponent

Move decimal right (large numbers)

Negative Exponent

Move decimal left (small numbers)

Significant Figures

Preserved in coefficient

Number Types

Very Large ( n > 0)

Greater than 10

1.5 x 10⁶ = 1,500,000

Normal Range ( n = 0)

Between 1 and 10

5.5 x 10⁰ = 5.5

Very Small ( n < 0)

Less than 1

3.2 x 10⁻⁴ = 0.00032

Tips & Tricks

Count decimal places moved to find exponent

Moving right = positive exponent

Moving left = negative exponent

Keep significant figures in coefficient

Use for very large or very small numbers

Understanding Standard Form

What is Standard Form?

Standard form (also called scientific notation) is a way of writing very large or very small numbers in a compact form. It expresses numbers as a product of a coefficient between 1 and 10 and a power of 10.

General Formula

a = b x 10ⁿ

  • a: The original number
  • b: Coefficient ( 1 ≤ b < 10)
  • n: Integer exponent

Why Use Standard Form?

  • Simplifies writing very large numbers
  • Makes very small numbers easier to read
  • Facilitates scientific calculations
  • Clearly shows significant figures
  • Enables easier comparison of magnitudes

Converting Steps

  1. Move decimal to create coefficient between 1 and 10
  2. Count decimal places moved
  3. Use count as exponent (positive for right, negative for left)
  4. Write in form b x 10ⁿ