Please enter a valid number.
Supports integers, decimals, and negative numbers
Coefficient must be a number (≥1 and <10 for standard form).
Please enter an integer exponent.
Positive = large number, negative = small number
Scientific Notation
—
Was this calculator helpful?
Sources & Methodology
Scientific notation rules follow IEEE 754 floating-point standards and NIST Guidelines for Expressing the Uncertainty of Measurement Results.
NIST — SI Units and Scientific Notation Guidelines
National Institute of Standards and Technology — authoritative rules for writing numbers in scientific notation in physics and engineering
Khan Academy — Scientific Notation Review
Curriculum-aligned explanation of scientific notation rules, conversion steps, and worked examples used as reference for step-by-step output
Methodology: To convert to scientific notation: parse the decimal value, find the order of magnitude (floor of log base 10 of the absolute value), divide to get the coefficient (must satisfy 1 ≤ |a| < 10), and output a × 10^n. For the reverse: multiply coefficient by 10^n using string manipulation to avoid floating-point drift on very large/small exponents. E notation is generated as aEn.
⏱ Last reviewed: April 2026
How to Convert Numbers to Scientific Notation
Scientific notation is the universal standard for expressing very large or very small numbers in science, engineering, and mathematics. Instead of writing 0.000000000167 or 602,200,000,000,000,000,000,000, scientists write 1.67 × 10⁻¹¹ and 6.022 × 10²³. The format keeps numbers manageable without losing precision.
The Scientific Notation Format
a × 10^n where 1 ≤ |a| < 10 and n is an integer
a = the coefficient (a number between 1 and 10, not including 10)
n = the exponent (positive for numbers ≥10, negative for numbers <1)
Examples:
45,000 = 4.5 × 10⁴
0.00032 = 3.2 × 10⁻⁴
-7,600,000 = -7.6 × 10⁶
n = the exponent (positive for numbers ≥10, negative for numbers <1)
Examples:
45,000 = 4.5 × 10⁴
0.00032 = 3.2 × 10⁻⁴
-7,600,000 = -7.6 × 10⁶
Step-by-Step Conversion: Number to Scientific Notation
Follow these three steps for any number:
- Step 1: Move the decimal point until you have a number between 1 and 10.
- Step 2: Count how many places you moved the decimal point.
- Step 3: If you moved left (big number), the exponent is positive. If you moved right (small number), the exponent is negative.
Common Scientific Notation Examples
| Standard Number | Scientific Notation | E Notation | Used for |
|---|---|---|---|
| 1,000 | 1 × 10³ | 1E3 | One thousand |
| 299,792,458 | 2.998 × 10⁸ | 2.998E8 | Speed of light (m/s) |
| 0.001 | 1 × 10⁻³ | 1E-3 | One thousandth |
| 0.000000001 | 1 × 10⁻⁹ | 1E-9 | 1 nanometer |
| 6.022 × 10²³ | 6.022 × 10²³ | 6.022E23 | Avogadro’s number |
| 1.602 × 10⁻¹⁹ | 1.602 × 10⁻¹⁹ | 1.602E-19 | Electron charge (C) |
| 9,460,000,000,000,000 | 9.46 × 10¹⁵ | 9.46E15 | Light-year (meters) |
Scientific Notation vs E Notation
Scientific notation (a × 10^n) and E notation (aEn) represent exactly the same value. E notation is used in calculators, spreadsheets, and programming languages because keyboards cannot easily type superscripts. For example, Excel displays 3,500,000 as 3.5E6, and Python prints 0.0000001 as 1e-07. They are interchangeable — this calculator shows both formats.
Multiplying and Dividing in Scientific Notation
Multiply: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n)
Example: (3 × 10⁴) × (2 × 10³) = 6 × 10⁷
If the coefficient exceeds 10, adjust: 15 × 10⁴ = 1.5 × 10⁵
If the coefficient exceeds 10, adjust: 15 × 10⁴ = 1.5 × 10⁵
Divide: (a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m-n)
Example: (8 × 10⁶) ÷ (4 × 10²) = 2 × 10⁴
💡 Significant figures tip: The number of digits in the coefficient represents the number of significant figures. 4.50 × 10³ has 3 significant figures; 4.5 × 10³ has 2. Always match your coefficient precision to the precision of your original measurement.
Frequently Asked Questions
Move the decimal point to get a coefficient between 1 and 10. Count the number of places moved — that is the exponent. Moving left gives a positive exponent (large number); moving right gives a negative exponent (small number). Example: 45,000 → move decimal 4 places left → 4.5 × 10⁴.
Scientific notation is a standard way to write very large or very small numbers as a × 10^n, where the coefficient a satisfies 1 ≤ |a| < 10 and n is any integer. It simplifies calculations and clearly shows the order of magnitude. Used universally in science, engineering, and mathematics.
0.00045 in scientific notation is 4.5 × 10⁻⁴. Move the decimal point 4 places right to get the coefficient 4.5. Because you moved right (the number is less than 1), the exponent is negative: -4.
6,000,000 in scientific notation is 6 × 10⁶. Move the decimal point 6 places left to get coefficient 6.0. Because the number is greater than 1 and you moved left, the exponent is positive: 6.
If the exponent is positive, move the decimal right by that many places (fills in zeros). If the exponent is negative, move the decimal left by that many places (adds leading zeros). Example: 3.2 × 10⁻⁴ → move decimal 4 places left → 0.00032.
They represent the same value written differently. Scientific notation: 3.5 × 10⁷. E notation: 3.5E7. E notation is used in calculators, programming (Python, JavaScript, C), and spreadsheets because superscripts are not available on standard keyboards. They are completely interchangeable.
A negative exponent means the number is less than 1. For example, 10⁻³ = 0.001. So 5 × 10⁻³ = 0.005. The negative exponent tells you how many places to move the decimal point left when converting back to standard form.
Multiply the coefficients and add the exponents: (a × 10^m) × (b × 10^n) = (a × b) × 10^(m+n). If the resulting coefficient is 10 or greater, shift it: 12 × 10⁴ = 1.2 × 10⁵. If it falls below 1, shift the other way: 0.5 × 10⁴ = 5 × 10³.
0.0000001 in scientific notation is 1 × 10⁻⁷. Count 7 decimal places to the right to reach 1.0, so the exponent is -7. This represents one ten-millionth, also written as 1E-7 in E notation.
Scientific notation is used because it makes enormous or tiny numbers manageable. The distance from Earth to Andromeda is about 2.365 × 10²⁰ meters — writing all those zeros would be error-prone and hard to read. It also explicitly shows significant figures and makes multiplication and division of large numbers straightforward by simply adding or subtracting exponents.
1,234,567 in scientific notation is 1.234567 × 10⁶. Move the decimal 6 places left to get coefficient 1.234567. The exponent is 6 because the original number is greater than 1 million (between 10⁶ and 10⁷).
0.000000001 (one billionth) in scientific notation is 1 × 10⁻⁹. This is the scale of a nanometer (1 nm = 10⁻⁹ meters) and is a common value in nanotechnology and atomic physics. Move the decimal 9 places right to reach 1.0, giving exponent -9.
Related Calculators
Popular Calculators
Aspect Ratio Calculator
Math
Fraction to Percent Calculator
Math
Golf Altitude Calculator
Math
Hours to Time Calculator
Math
Stripe Fee Calculator
Finance
Pain & Suffering Calculator
Legal
TDEE Calculator
Health
Roofing Calculator
Construction
GPA Calculator
Education
Mortgage Refinance
Finance
CPM Calculator
Marketing
Markup Calculator
Finance