Scientific Notation Calculator
Convert any number to or from scientific notation (standard form) instantly. Enter a decimal number to express it as a × 10n, or paste E notation to get the expanded decimal value. Adjust significant figures for the precision you need.
Scientific Notation Calculator
Calculator
How it works
To convert to scientific notation, move the decimal point until you have a number between 1 and 10, then multiply by 10 raised to the power of the number of places moved.
Understanding Scientific Notation
Scientific notation is a mathematical system for expressing numbers that are extremely large or extremely small. Every number written in scientific notation follows the form a × 10n, where a (the coefficient or significand) satisfies 1 ≤ |a| < 10, and n (the exponent) is an integer that indicates how many places the decimal point has been shifted. This concise representation eliminates long strings of trailing or leading zeros while preserving the number of significant figures. Scientists, engineers, and mathematicians rely on scientific notation daily to communicate measurements that span dozens of orders of magnitude, from subatomic particle masses to astronomical distances.
Converting to Scientific Notation
To convert a standard decimal number into scientific notation, move the decimal point until only one non-zero digit remains to its left. Count the number of places you moved the decimal. If you shifted the decimal to the left, the exponent n is positive; if you shifted it to the right, the exponent n is negative. For example, 4,560,000 becomes 4.56 × 106 (decimal moved 6 places left), while 0.000089 becomes 8.9 × 10-5 (decimal moved 5 places right).
Converting from Scientific Notation
Reverse the process to expand scientific notation back to a standard number. A positive exponent means you move the decimal point to the right, adding zeros as needed. A negative exponent means you move it to the left. For instance, 3.07 × 104 becomes 30,700, and 5.2 × 10-3 becomes 0.0052.
Very Large and Very Small Numbers
Scientific notation truly shines when working with quantities at extreme scales. The observable universe is roughly 8.8 × 1026 metres across, while a single proton has a diameter of about 1.7 × 10-15 metres. Writing these values in decimal form would require dozens of digits and is impractical for calculations. Scientific notation lets you compare magnitudes at a glance by simply comparing the exponents.
Engineering Notation (Powers of 3)
Engineering notation is a specialized variant where the exponent is always restricted to a multiple of three (... -6, -3, 0, 3, 6, 9 ...). This convention maps directly to the SI metric prefixes: kilo (103), mega (106), giga (109), milli (10-3), micro (10-6), and nano (10-9). For example, a 4,700-ohm resistor is written as 4.7 × 103 ohms (4.7 kΩ) in engineering notation. The coefficient in engineering notation can range from 1 to 999 rather than 1 to 9.99.
E Notation in Computing
Because superscript formatting is unavailable on most keyboards, computers and calculators use E notation to represent scientific notation. The letter “E” (or “e”) replaces “× 10^”. For example, 1.23 × 108 is entered as 1.23E8 or 1.23e8. This notation appears in virtually every programming language (C, C++, Java, Python, JavaScript), spreadsheet applications (Excel, Google Sheets), and scientific data-exchange formats such as CSV and JSON. When reading E notation, remember that the number after E is the power of ten, not a multiplier itself.
Scientific Notation Reference Table
The table below lists well-known physical constants and measurements in scientific notation, demonstrating how this format handles numbers across many orders of magnitude.
| Quantity | Decimal Value | Scientific Notation | E Notation |
|---|---|---|---|
| Speed of light | 299,792,458 m/s | 2.998 × 108 | 2.998E8 |
| Avogadro's number | 602,214,076,000,000,000,000,000 | 6.022 × 1023 | 6.022E23 |
| Electron mass | 0.000...0009109 kg (31 zeros) | 9.109 × 10-31 | 9.109E-31 |
| Earth's mass | 5,972,000,000,000,000,000,000,000 kg | 5.972 × 1024 | 5.972E24 |
| Planck's constant | 0.000...000663 J·s (34 zeros) | 6.626 × 10-34 | 6.626E-34 |
| Distance to Andromeda | 2.537 × 1022 m | 2.537 × 1022 | 2.537E22 |
| Hydrogen atom radius | 0.000000000053 m | 5.3 × 10-11 | 5.3E-11 |
| US national debt (approx.) | $34,000,000,000,000 | 3.4 × 1013 | 3.4E13 |
How to Convert to Scientific Notation
Follow these step-by-step worked examples to master converting any number into scientific notation. The key rule is that the coefficient must always be between 1 and 10.
Example 1: Convert 186,000 to scientific notation
- Identify the first non-zero digit: 1
- Place the decimal after it: 1.86000
- Count the places moved: the decimal moved 5 places to the left
- The exponent is +5 (left shift = positive)
- Drop trailing zeros: 1.86 × 105
Result: 186,000 = 1.86 × 105
Example 2: Convert 0.000742 to scientific notation
- Identify the first non-zero digit: 7
- Place the decimal after it: 7.42
- Count the places moved: the decimal moved 4 places to the right
- The exponent is -4 (right shift = negative)
Result: 0.000742 = 7.42 × 10-4
Example 3: Convert 53,400,000,000 to scientific notation
- Identify the first non-zero digit: 5
- Place the decimal after it: 5.3400000000
- Count the places moved: the decimal moved 10 places to the left
- The exponent is +10 (left shift = positive)
- Drop trailing zeros: 5.34 × 1010
Result: 53,400,000,000 = 5.34 × 1010
Frequently Asked Questions
Frequently Asked Questions
Was this calculator helpful?
Your rating helps other students discover this tool.
Related Calculators
Explore other calculators to help with your academic planning and success.
