Standard Form Calculator

Convert positive or negative numbers to standard form as a decimal multiplied by a power of 10.

Convert numbers to standard form (scientific notation). Express as a decimal between 1 and 10 multiplied by a power of 10.

Enter any number
? × 10^?
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help_outlineHow to Useexpand_more

Converting Numbers to Standard Form

Standard form makes very large or very small numbers easier to read and work with. It's commonly used in science and engineering to express quantities like the speed of light (671,000,000 mph = 6.71 × 10⁸).

Step-by-Step Conversion Process:

  1. Move the decimal point until only one non-zero digit is to the left
  2. The resulting decimal number becomes your coefficient (a)
  3. Count how many places you moved the decimal - this is your exponent (b)
  4. If you moved left, b is positive; if you moved right, b is negative
  5. Write the result as a × 10^b

About Trailing Zeros:

Remove trailing zeros only if they were originally to the left of the decimal point. Trailing zeros to the right of the decimal are significant figures and should be preserved.

infoWhat is Standard Form Calculator?expand_more

Standard form is a method of writing numbers as a decimal multiplied by a power of 10. It's particularly useful for expressing very large numbers (like astronomical distances) or very small numbers (like molecular sizes) in a compact, readable format.

The standard form format is a × 10^b where:

  • a is a decimal number where 1 ≤ |a| < 10 (the absolute value is at least 1 but less than 10)
  • b is an integer representing the power of 10 needed to equal the original number

Standard form is essentially the same as scientific notation. The term "standard form" is commonly used in the UK and other countries, while "scientific notation" is the preferred term in the United States.

functionsFormulaexpand_more

Standard Form Format:

a × 10^b

where 1 ≤ |a| < 10 and b is an integer

Determining the Exponent:

• Count decimal places moved to get coefficient between 1 and 10

• Moved decimal left → positive exponent (large numbers)

• Moved decimal right → negative exponent (small numbers)

• No movement needed → exponent is 0

Reading Standard Form:

4.59608 × 10^5 is read as "4.59608 times 10 to the power of 5"

This equals 459,608

lightbulbExamplesexpand_more

Example 1: Convert 459,608 to Standard Form

Move decimal 5 places to the left: 4.59608

Coefficient a = 4.59608

Moved left, so exponent b = 5 (positive)

Result: 4.59608 × 10⁵

Example 2: Convert 0.000380 to Standard Form

Move decimal 4 places to the right: 3.80

Coefficient a = 3.80 (trailing zero preserved - it's significant)

Moved right, so exponent b = -4 (negative)

Result: 3.80 × 10⁻⁴

Example 3: Speed of Light

Speed of light ≈ 671,000,000 miles per hour

Move decimal 8 places to the left: 6.71

Result: 6.71 × 10⁸ mph

quizFAQexpand_more
What's the difference between standard form and scientific notation?expand_more
They are essentially the same thing. 'Standard form' is the term commonly used in the UK and some other countries, while 'scientific notation' is the preferred term in the United States. Both express numbers as a coefficient (between 1 and 10) multiplied by a power of 10.
Why must the coefficient be between 1 and 10?expand_more
This convention ensures every number has exactly one standard form representation. Without this rule, 300 could be written as 3×10², 30×10¹, 0.3×10³, etc. The constraint 1 ≤ |a| < 10 creates a unique, standardized format.
How do I handle trailing zeros?expand_more
Only remove trailing zeros if they were to the LEFT of the original decimal point (they're not significant). Keep trailing zeros that were to the RIGHT of the decimal point, as they represent significant figures. For example, 0.000380 becomes 3.80 × 10⁻⁴, not 3.8 × 10⁻⁴.
What does a negative exponent mean?expand_more
A negative exponent indicates the number is less than 1. Each negative power of 10 represents moving the decimal one place to the left: 10⁻¹ = 0.1, 10⁻² = 0.01, 10⁻³ = 0.001. So 3.8 × 10⁻⁴ = 0.00038.
Can negative numbers be written in standard form?expand_more
Yes! Negative numbers follow the same rules. The negative sign stays with the coefficient. For example, -459,608 becomes -4.59608 × 10⁵. The exponent remains positive because it describes magnitude, not sign.