Standard Form Calculator

Convert to Standard Form

Enter a number to convert it to standard form (scientific notation) or vice versa.

Please enter a valid number.

How to Calculate Standard Form

Standard form, also known as scientific notation, is a way of writing very large or very small numbers in a more concise format. It's widely used in scientific and engineering fields.

Formula

The general formula for standard form is:

\[ a \times 10^n \]

Where:

  • \(a\) is a number between 1 and 10
  • \(n\) is an integer (positive or negative)

Calculation Steps

  1. Identify the number you want to convert
  2. Move the decimal point left or right until you have a number between 1 and 10
  3. Count how many places you moved the decimal point
  4. Write the number in the form \(a \times 10^n\), where \(a\) is the number between 1 and 10, and \(n\) is how many places you moved the decimal point (positive if you moved it left, negative if you moved it right)

Example

Let's convert 45,000 to standard form:

  1. The number is 45,000
  2. Move the decimal point 4 places to the left: 4.5000
  3. We moved the decimal point 4 places
  4. Therefore, 45,000 in standard form is \(4.5 \times 10^4\)

Visual Representation

Original Number: 45,000 Move decimal 4 places left: 4.5|000 ← 4 places Standard Form: 4.5 × 10⁴ Original Number Decimal Movement Final Result

This diagram illustrates how 45,000 is represented in standard form as 4.5 × 10^4.

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