Scientific Notation Converter
Convert any number to and from scientific notation, plus engineering notation and E-notation, with the order of magnitude and expanded standard form.
Como usar esta calculadora
- 1Enter any number — plain like 6500000 or 0.00042, or already in E-notation like 6.5e6.
- 2Optionally set how many significant figures to keep in the coefficient.
- 3Read the scientific, engineering, and E-notation forms.
- 4Use the order of magnitude to compare the size of two numbers quickly.
Como funciona
Scientific notation
value = m × 10ⁿ, with 1 ≤ |m| < 10 n = ⌊log₁₀|value|⌋ (the order of magnitude) m = value ÷ 10ⁿ (the coefficient) engineering notation: n restricted to multiples of 3
Scientific notation expresses any number as a coefficient m, between 1 and 10, multiplied by a power of ten. The exponent n is the order of magnitude — the whole number of places the decimal point must move — found by taking the floor of the base-ten logarithm. Dividing the original value by 10ⁿ leaves the coefficient. This format has two big advantages: it makes very large and very small numbers readable at a glance without counting zeros, and it makes their relative size obvious, since comparing exponents compares orders of magnitude directly. Engineering notation is a variant that keeps the exponent a multiple of three, so it aligns with the metric prefixes that step in thousands.
Exemplo resolvido
The number 12,345 becomes 1.2345 × 10⁴, because the decimal point moves four places left to leave a coefficient between 1 and 10. A tiny number like 0.00042 becomes 4.2 × 10⁻⁴, with a negative exponent counting places to the right.
Scientific Notation Converter: o guia completo
Why scientists write numbers this way
Scientific notation exists to tame numbers that are otherwise unwieldy. The mass of an electron is about 0.00000000000000000000000000000091 kilograms, and the number of molecules in a mole is roughly 602,000,000,000,000,000,000,000. Writing these out invites errors — miscount the zeros and you are off by a factor of ten. Expressed as 9.1 × 10⁻³¹ and 6.02 × 10²³, they become compact, checkable, and easy to say aloud.
The format also separates two independent pieces of information: the significant figures, carried by the coefficient, and the scale, carried by the exponent. This separation is why scientific notation dovetails so neatly with the idea of significant figures and measurement precision. A physicist reading 3.00 × 10⁸ knows both the value (the speed of light) and that it is quoted to three significant figures, information that '300000000' hides.
Order of magnitude and quick comparison
The exponent in scientific notation is the order of magnitude, and it is a powerful tool for rough reasoning. Two quantities that differ by one order of magnitude differ by a factor of ten; by three orders, a factor of a thousand. Comparing exponents lets you see instantly that a bacterium (about 10⁻⁶ metres) is roughly a hundred times smaller than a human hair (about 10⁻⁴ metres) without doing any arithmetic on the coefficients.
This is the basis of order-of-magnitude estimation, a skill physicists and engineers prize: getting an answer right to the nearest power of ten is often enough to know whether a plan is sensible, a measurement is plausible, or a result is wildly wrong. Scientific notation makes those estimates natural, because the scale of every quantity is written explicitly in its exponent rather than buried in a row of zeros.
Engineering notation and the metric prefixes
Engineering notation is a close cousin of scientific notation with one extra rule: the exponent must be a multiple of three. This seemingly small change makes it line up perfectly with the metric system's prefixes, which also step in thousands — kilo (10³), mega (10⁶), giga (10⁹) going up, and milli (10⁻³), micro (10⁻⁶), nano (10⁻⁹) going down. A value written as 47 × 10³ ohms is immediately read as 47 kilohms.
This is why electronics and engineering favour it: component values, frequencies, and data rates map directly onto spoken units. The coefficient in engineering notation can be anywhere from 1 up to just under 1000, rather than the strict 1-to-10 range of scientific notation, which is the price of keeping the exponent tied to the prefixes. E-notation, meanwhile — the '1.2345e4' form — is simply how computers and calculators type scientific notation on a single line, since they cannot render a raised exponent.
Perguntas frequentes
How do I convert a number to scientific notation?
Move the decimal point until only one non-zero digit remains in front of it; that gives the coefficient. The number of places you moved is the exponent — positive if you moved left, negative if right. So 12,345 becomes 1.2345 × 10⁴ and 0.00042 becomes 4.2 × 10⁻⁴.
What is the difference between scientific and engineering notation?
Scientific notation keeps the coefficient between 1 and 10 with any integer exponent. Engineering notation restricts the exponent to multiples of three so it lines up with metric prefixes like kilo and mega, letting the coefficient range from 1 up to just under 1000.
What is E-notation?
E-notation is how calculators and computers write scientific notation on one line, using the letter e for 'times ten to the power of'. So 1.2345e4 means 1.2345 × 10⁴. It exists because a screen or keyboard can't render a raised superscript exponent.
What is an order of magnitude?
The order of magnitude is the power of ten in a number's scientific notation — essentially its scale. Numbers one order of magnitude apart differ by a factor of ten. Comparing orders of magnitude is a fast way to judge how much bigger one quantity is than another.