Scientific Notation Calculator & Converter: b ร 10โฟ Lab
Free scientific notation calculator. Convert real numbers to scientific, E-, and engineering notation. Add, subtract, multiply, divide, power, and square root with step-by-step Logic Trace. Precision control. No sign-upโall calculations run locally.
What This Scientific Notation Lab Does
This scientific notation calculator provides a converter (real number โ scientific, E-notation, engineering) and a notation calculator with operands X and Y in b ร 10n form. Operations include X+Y, XโY, XรY, XรทY, X^y, and โx. The Logic Trace shows for add/subtract: exponent alignment and significand combination; for multiply/divide: product or quotient of significands and exponents; and always the final normalization (1 โค |b| < 10). Set Precision (digits after decimal) from 1 to 50. All calculations run locally in your browserโno data is sent to servers.
Scientific Notation, E-Notation & Engineering Notation
In scientific notation, a number is written as b ร 10n, where the significand b satisfies 1 โค |b| < 10 and n is an integer exponent. For example: 6,000,000 = 6 ร 106; 0.00004 = 4 ร 10โ5. E-notation (or e-notation) abbreviates this as beยฑnโe.g., 6e6, 4eโ5โand is standard in calculators and programming. Engineering notation keeps exponents as multiples of 3 (10ยณ, 10โถ, 10โปโน) to align with SI prefixes like kilo, mega, and micro.
When to Use Scientific Notation
Use scientific notation when numbers are very large (e.g., Avogadro's number 6.022 ร 10ยฒยณ, astronomical distances) or very small (e.g., Planck constant scale, wavelengths, atomic masses). Physics, chemistry, astronomy, and engineering routinely rely on it. This calculator helps students verify homework, prepare for exams, and professionals quickly convert between decimal and scientific forms with configurable precision.
Scientific Notation Calculator FAQ
? What is scientific notation?
Scientific notation writes numbers as b ร 10n, where the significand b satisfies 1 โค |b| < 10 and n is an integer. Examples: 1,500,000 = 1.5 ร 106; 0.000023 = 2.3 ร 10โ5. This compact form simplifies very large and small numbers.
? What is E-notation?
E-notation is a shorthand for scientific notation: ben means b ร 10n. For example, 1.5e6 = 1.5 ร 106 and 2.3eโ5 = 2.3 ร 10โ5. Commonly used in calculators, spreadsheets, and programming.
? What is engineering notation?
Engineering notation uses exponents that are multiples of 3 (thousands, millions, billionths), aligning with SI prefixes. Example: 15,000 = 15 ร 103 (15 kilo); 0.000045 = 45 ร 10โ6 (45 micro). The significand may be 1โ999 instead of 1โ9.99.
? How do you convert a number to scientific notation?
Find the power of 10: n = floor(logโโ|x|). Divide the number by 10n to get the significand b (1 โค |b| < 10). Result: b ร 10n. Example: 6,000,000 โ n=6, b=6 โ 6 ร 106. Use the Converter above for instant results.
? How do you add numbers in scientific notation?
Align exponents first (use the larger exponent), then add the significands. Example: 8 ร 10โ1 + 5 ร 102 โ 0.008 ร 102 + 5 ร 102 = 5.008 ร 102. The Logic Trace shows each step: alignment, combination, and normalization.
? How do you multiply and divide in scientific notation?
Multiplication: multiply significands, add exponents โ (bโ ร 10nโ)(bโ ร 10nโ) = (bโ ร bโ) ร 10nโ+nโ. Division: divide significands, subtract exponents โ (bโ ร 10nโ)/(bโ ร 10nโ) = (bโ/bโ) ร 10nโโnโ. Normalize so 1 โค |b| < 10.