Scientific Notation Calculator
Add, subtract, multiply, and divide numbers in scientific notation, E notation, or standard form. Get results in all three formats instantly.
Calculate with Scientific Notation
Scientific Notation Prefix Reference
| Prefix | Symbol | Power | Value | Example |
|---|---|---|---|---|
| Tera | T | 10¹² | 1,000,000,000,000 | 1.5e12 |
| Giga | G | 10⁹ | 1,000,000,000 | 2.4e9 |
| Mega | M | 10⁶ | 1,000,000 | 5.0e6 |
| Kilo | k | 10³ | 1,000 | 3.5e3 |
| Milli | m | 10⁻³ | 0.001 | 4.2e-3 |
| Micro | μ | 10⁻⁶ | 0.000001 | 8.0e-6 |
| Nano | n | 10⁻⁹ | 0.000000001 | 1.6e-9 |
| Pico | p | 10⁻¹² | 0.000000000001 | 6.0e-12 |
How Scientific Notation Works
Scientific notation is the standard method for expressing very large and very small numbers. Any number is written as the product of a decimal between 1 and 10 and a power of 10.
Converting to Scientific Notation
To convert a large number like 93,000,000 to scientific notation, count how many places you move the decimal point to the left until you have a number between 1 and 10. Moving it 7 places gives 9.3, so the result is 9.3 × 10⁷. For small numbers like 0.00045, move the decimal right 4 places to get 4.5, giving 4.5 × 10⁻⁴.
Input Formats This Calculator Accepts
- Standard notation: 122500
- E notation: 1.225e5 or 1.225E5
- Scientific notation: 1.225×10^5 or 1.225×10^5
- Negative exponents: 3.5e-4
Rules for Arithmetic in Scientific Notation
For multiplication, multiply the coefficients and add the exponents. For division, divide the coefficients and subtract the exponents. For addition and subtraction, first align the exponents, then add or subtract the coefficients. This calculator handles all alignment automatically.
Significant Figures in Scientific Notation
Significant figures in scientific notation indicate the precision of a measurement. The number of digits in the coefficient tells you how many significant figures the value has.
When to Use Auto Significant Figures
Auto significant figures mode counts the sig figs in each input and applies the appropriate precision to the result. This is correct for most measured values in science and engineering.
When to Turn Off Auto Significant Figures
Turn off auto sig figs when one of your values is an exact count or a defined constant. For example, when multiplying a measured value by the exact constant 2 (as in d = 2r), the 2 has infinite precision and should not limit your result to one significant figure.
E Notation vs Engineering Notation
E notation and scientific notation are equivalent, only the symbol changes. Engineering notation is different: it restricts exponents to multiples of 3 to align with metric prefixes. For example, 4,875,000 is 4.875 × 10⁶ in scientific notation and 4875 × 10³ (4875 kilo) in engineering notation.
Frequently Asked Questions
Scientific notation expresses a number as a decimal between 1 and 10 multiplied by a power of 10. For example, 4,500,000 becomes 4.5 × 10⁶ and 0.000045 becomes 4.5 × 10⁻⁵. It is used in science to manage very large and very small numbers.
To add numbers in scientific notation, first convert both numbers to the same power of 10, then add the decimal parts. For example, 3 × 10⁴ plus 2 × 10³ becomes 30 × 10³ plus 2 × 10³ equals 32 × 10³, which is 3.2 × 10⁴.
Multiply the decimal coefficients together and add the exponents. For example, (3 × 10⁴) multiplied by (2 × 10³) gives 6 × 10⁷. If the resulting coefficient is 10 or greater, increase the exponent by one and adjust the decimal.
E notation is the same as scientific notation but uses the letter E instead of “times 10 to the power.” For example, 4.5 × 10⁶ is written as 4.5E6 or 4.5e6. It is commonly used in calculators, spreadsheets, and programming languages.
Engineering notation uses only powers of 10 that are multiples of 3, such as 10³, 10⁶, and 10⁹. This aligns with SI prefixes like kilo, mega, and giga, making it practical for electrical and physical measurements.
Yes. You can enter ordinary numbers like 122500 alongside scientific notation like 3.655e3 and the calculator will convert and compute correctly. All formats can be mixed in a single calculation.