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Scientific Notation Converter Examples
The Scientific Notation Converter converts numbers between standard decimal notation and scientific notation. Below are examples covering common use cases in science, engineering, and programming.
Standard to Scientific Notation
Convert large numbers to scientific notation:
Standard Scientific Notation
6,000,000 6 × 10⁶
93,000,000 9.3 × 10⁷
299,792,458 2.99792458 × 10⁸
1,000,000,000 1 × 10⁹
5,970,000,000,000,000,000,000,000 5.97 × 10²⁴ (mass of Earth in kg)
Standard to Scientific Notation — Small Numbers
Convert small numbers to scientific notation:
Standard Scientific Notation
0.000045 4.5 × 10⁻⁵
0.001 1 × 10⁻³
0.0000000167 1.67 × 10⁻⁸
0.000000000000001 1 × 10⁻¹⁵
Scientific to Standard Notation
Convert scientific notation back to decimal:
Scientific Notation Standard
3.14 × 10³ 3,140
6.022 × 10²³ 602,200,000,000,000,000,000,000
1.67 × 10⁻²⁷ 0.00000000000000000000000000167
9.11 × 10⁻³¹ 0.000000000000000000000000000000911
Engineering Notation
Engineering notation uses exponents that are multiples of 3 (matching SI prefixes):
Standard Scientific Engineering
6,000,000 6 × 10⁶ 6 × 10⁶ (6 mega-)
45,000 4.5 × 10⁴ 45 × 10³ (45 kilo-)
0.000045 4.5 × 10⁻⁵ 45 × 10⁻⁶ (45 micro-)
0.0000000023 2.3 × 10⁻⁹ 2.3 × 10⁻⁹ (2.3 nano-)
SI Prefix Equivalents
Powers of 10 and their SI prefix names:
Power Prefix Symbol Example
10¹² tera T 1 TB = 1 × 10¹² bytes
10⁹ giga G 1 GHz = 1 × 10⁹ Hz
10⁶ mega M 1 MW = 1 × 10⁶ watts
10³ kilo k 1 km = 1 × 10³ meters
10⁻³ milli m 1 mm = 1 × 10⁻³ meters
10⁻⁶ micro μ 1 μs = 1 × 10⁻⁶ seconds
10⁻⁹ nano n 1 nm = 1 × 10⁻⁹ meters
10⁻¹² pico p 1 pF = 1 × 10⁻¹² farads
Significant Figures Control
Specify the number of significant figures in the coefficient:
Number: 299,792,458 (speed of light in m/s)
1 sig fig: 3 × 10⁸
2 sig figs: 3.0 × 10⁸
3 sig figs: 3.00 × 10⁸
4 sig figs: 2.998 × 10⁸
9 sig figs: 2.99792458 × 10⁸ (exact)
The number of significant figures indicates measurement precision.
E Notation (Programming)
E notation used in programming languages:
Scientific Notation E Notation Language
6 × 10⁶ 6E6 JavaScript, Python, Java
4.5 × 10⁻⁵ 4.5E-5 C, C++, Fortran
1.67 × 10⁻²⁷ 1.67e-27 Python, Ruby
6.022 × 10²³ 6.022e23 All languages
JavaScript example:
const speedOfLight = 2.998e8; // meters per second
const electronMass = 9.11e-31; // kilograms
Python example:
avogadro = 6.022e23
planck = 6.626e-34
Scientific Constants in Scientific Notation
Constant Value
Speed of light (c) 2.998 × 10⁸ m/s
Avogadro's number (Nₐ) 6.022 × 10²³ mol⁻¹
Planck's constant (h) 6.626 × 10⁻³⁴ J·s
Electron mass (mₑ) 9.109 × 10⁻³¹ kg
Proton mass (mₚ) 1.673 × 10⁻²⁷ kg
Gravitational constant (G) 6.674 × 10⁻¹¹ N·m²/kg²
Boltzmann constant (kB) 1.381 × 10⁻²³ J/K
Arithmetic with Scientific Notation
Multiply and divide numbers in scientific notation:
Multiplication:
(3 × 10⁴) × (2 × 10³)
= (3 × 2) × 10^(4+3)
= 6 × 10⁷
Division:
(8 × 10⁶) ÷ (4 × 10²)
= (8 ÷ 4) × 10^(6-2)
= 2 × 10⁴
Addition (same exponent):
(3.5 × 10⁴) + (1.2 × 10⁴)
= (3.5 + 1.2) × 10⁴
= 4.7 × 10⁴
Addition (different exponents — align first):
(3.5 × 10⁴) + (1.2 × 10³)
= (3.5 × 10⁴) + (0.12 × 10⁴)
= 3.62 × 10⁴
Parts-Per Notation Conversion
Notation Meaning Scientific Notation
1 ppm 1 per million 1 × 10⁻⁶
1 ppb 1 per billion 1 × 10⁻⁹
1 ppt 1 per trillion 1 × 10⁻¹²
Example: Water quality standard of 10 ppb lead
10 ppb = 10 × 10⁻⁹ = 1 × 10⁻⁸ (1 part per 100 million)
- Convert any decimal number to scientific notation
- Convert scientific notation back to standard decimal
- Engineering notation with exponents as multiples of 3
- SI prefix equivalents (kilo, mega, giga, milli, micro, nano)
- Control the number of significant figures in the coefficient
- E notation for programming languages (6E6, 4.5e-5)
- Arithmetic operations with scientific notation
- Parts-per notation (ppm, ppb, ppt) conversion