Scientific Notation Calculator (Standard & Engineering Form)
By Santaji GadepatilinUpdated November 7, 2026
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten, so 45,600,000 becomes 4.56 × 10⁷. This scientific notation calculator splits any number into its coefficient and exponent, gives the engineering-notation form whose exponent is a multiple of three, and converts back to an ordinary decimal.
How to use the scientific notation calculator
Enter a number in ordinary decimal form (you can also type E notation such as 6.02e23). The calculator returns the exponent and coefficient of its scientific notation and the matching engineering notation. To convert back, enter a coefficient and exponent and the decimal number is filled in.
Scientific notation formula
x = a × 10ⁿ with n = ⌊log₁₀|x|⌋ and a = x ÷ 10ⁿ
Engineering: neng = 3 × ⌊n ÷ 3⌋ · aeng = x ÷ 10neng
Worked example
Convert 45,600,000:
- log₁₀(45,600,000) = 7.6590, so the exponent is 7
- Coefficient = 45,600,000 ÷ 10⁷ = 4.56 → 4.56 × 10⁷ (E notation 4.56E7)
- Engineering exponent = 3 × ⌊7 ÷ 3⌋ = 6, coefficient 45.6 → 45.6 × 10⁶ = 45.6 mega
For a small number, 0.00045 → log₁₀ = −3.35, exponent −4, coefficient 4.5 → 4.5 × 10⁻⁴ (engineering 450 × 10⁻⁶ = 450 micro).
Examples in scientific and engineering notation
| Quantity | Scientific | E notation | Engineering |
|---|---|---|---|
| Speed of light (m/s) | 2.99792458 × 10⁸ | 2.99792458e8 | 299.792458 × 10⁶ |
| Avogadro constant (1/mol) | 6.02214076 × 10²³ | 6.02214076e23 | 602.214076 × 10²¹ |
| Earth–Sun distance (m) | 1.496 × 10¹¹ | 1.496e11 | 149.6 × 10⁹ |
| Elementary charge (C) | 1.602176634 × 10⁻¹⁹ | 1.602176634e-19 | 160.2176634 × 10⁻²¹ |
| 1 µF in farads | 1 × 10⁻⁶ | 1e-6 | 1 × 10⁻⁶ |
| Hydrogen atom radius (m) | 5.29 × 10⁻¹¹ | 5.29e-11 | 52.9 × 10⁻¹² |
| World population (approx.) | 8.1 × 10⁹ | 8.1e9 | 8.1 × 10⁹ |
| 0.00045 | 4.5 × 10⁻⁴ | 4.5e-4 | 450 × 10⁻⁶ |
Practical notes
- Zero has no scientific-notation exponent; it is written simply as 0.
- Significant figures are the digits in the coefficient: 4.560 × 10⁷ states four, 4.56 × 10⁷ three.
- Engineering exponents map to SI prefixes: 10³ kilo, 10⁶ mega, 10⁹ giga, 10⁻³ milli, 10⁻⁶ micro, 10⁻⁹ nano, 10⁻¹² pico.
Frequently asked questions
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit is left of it; the number of places moved is the exponent — positive if you moved left, negative if you moved right. 0.00045 becomes 4.5 × 10⁻⁴.
What is engineering notation?
Like scientific notation, but the exponent is always a multiple of 3 so it matches SI prefixes — 45.6 × 10⁶ is 45.6 mega. The coefficient is between 1 and 999.
What does 4.56E7 mean on a calculator?
E notation is scientific notation for screens and spreadsheets — 4.56E7 means 4.56 × 10⁷ = 45,600,000. A negative exponent such as 2E-3 means 0.002.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents, then renormalise. (3 × 10⁴) × (5 × 10³) = 15 × 10⁷ = 1.5 × 10⁸.