Numbers in physics, chemistry, and astronomy are written in a very specific form: a number between 1 and 10, times a power of ten. The speed of light is 3 \times 10^8 m/s. Avogadro's number is 6.022 \times 10^{23}. The mass of an electron is 9.1 \times 10^{-31} kg. Never 2^n. Never 3^n. Always ten.
Why ten? Is this just convention, or is there a deeper reason? The answer is both — convention with a very good reason behind it, and the reason explains why computer scientists often use 2^n instead, and why this is not a contradiction but a revealing choice.
The short answer
Scientific notation uses 10^n because we count in base 10, and in base 10 the digits of a number are already telling you its power of ten. Writing 30{,}000{,}000{,}000 as 3 \times 10^{10} is simply "keep the leading digit, count the other digits to get the exponent." No multiplication, no arithmetic. The notation is a direct repackaging of what you already see.
That is the whole reason. If humans had evolved with eight fingers, we would count in base 8, scientific notation would use 8^n, and 3 \times 10^{10} would look just as natural as 8^{12} does to someone fluent in base 8.
Why base 10 specifically
Nothing about the universe prefers 10 over any other number. We count in base 10 for a well-known reason: humans have ten fingers, and the earliest counting systems all built up from hand-counting. The Mesopotamians experimented with base 60, the Mayans used base 20 (ten fingers plus ten toes), and some cultures used base 12 (three knuckles on each of four fingers, counted with the thumb).
Once base 10 stabilised across most of the world's writing systems, every numerical convention piggy-backed on it. The metric system (deci, centi, milli, kilo, mega, giga, tera — each step a power of ten). Money (hundred paise in a rupee, hundred rupees in a note series). Scientific notation followed the same path, because the audience reading scientific notation was already fluent in base 10.
Why this choice is actually brilliant
Here is the deeper reason: in any positional number system, the position of a digit corresponds to a power of the base. In base 10,
The "10^n" is already built into how you write the number. Scientific notation just keeps the first digit and the exponent of the leading power of ten, dropping the middle digits for a compact form:
No arithmetic required. The exponent tells you how many digits are in the original number (minus one), and the leading coefficient tells you what the number starts with. That is why scientists chose this form — it is almost a free re-encoding of base 10.
Compare with using 2^n. To write 2{,}345 as a power of 2, you need \log_2 2345 \approx 11.19, so 2{,}345 \approx 2.22 \times 2^{10}. You cannot read this off from the digits; you have to compute a logarithm. Nobody does mental arithmetic with 2^n unless they are a computer scientist, because base 10 does not help you with it.
How to read scientific notation
Two rules to make the notation automatic.
- Big numbers: the exponent is positive, and it tells you how far the decimal point has moved to the left to leave a number between 1 and 10.
- 3 \times 10^8 = 3 followed by 8 zeros → 300{,}000{,}000. Move the decimal 8 places to the right.
- Small numbers: the exponent is negative, and its absolute value tells you how far the decimal point has moved to the right.
- 1.5 \times 10^{-3} = 0.0015. Move the decimal 3 places to the left.
Indian students often see an extra benefit: when you convert to the Indian number system (1 lakh = 10^5, 1 crore = 10^7), the power of 10 in scientific notation lines up directly with lakhs and crores. 3 \times 10^8 is 3 followed by 8 zeros, i.e. 30 crore. 6.022 \times 10^{23} is 6.022 followed by 23 zeros — a number so big that the Indian number system itself runs out of names around 10^{17}.
Where 2^n is used instead
Computer scientists and engineers switch to 2^n because computers fundamentally count in binary. Memory sizes, data speeds, and addressing use powers of two. That is why:
- A kilobyte used to be 2^{10} = 1024 bytes (though the modern standard is 10^3 = 1000 bytes, with 2^{10} renamed to "kibibyte" in technical specifications).
- A megabyte, gigabyte, terabyte in the binary sense are 2^{20}, 2^{30}, 2^{40} — not 10^6, 10^9, 10^{12}.
- Video resolutions and audio bit depths are powers of 2: 256 colours per channel (2^8), 65{,}536 (2^{16}), and so on.
But notice: even computer scientists do not write 2^{30} in general scientific communication. They convert to the nearest power of 10 for the sake of audiences who think in base 10: "this computer has about a billion transistors" is clearer than "2^{30} transistors" for someone outside the field. The base is chosen for the audience, not the physics.
Does the choice of base change the answer?
No. The number is the same either way; only the packaging differs.
Each row packages the same number in a different exponential form. Scientists use base 10 for convenience, computer scientists use base 2 for hardware alignment, and mathematicians often use base e for calculus (because derivatives of e^x are uniquely clean). All three are legitimate. All three describe the same numbers.
Why base e shows up in pure math: the derivative of e^x is e^x itself — it is the only exponential function that is its own rate of change. Every other base, like 10^x, has a derivative of 10^x \times \ln 10 \approx 2.303 \times 10^x, with an awkward constant out front. For calculus, base e is the clean choice. For writing down numbers in a way humans can read, base 10 wins.
The summary
Scientific notation uses 10^n because humans write numbers in base 10, and in base 10 the notation is an almost-free re-encoding. If we wrote numbers in base 2 or base 60, we would have "scientific notation" in that base instead, and the conversion rules would follow the digit structure of that base. The base of scientific notation is not a statement about the universe — it is a statement about the audience, which is us, the ten-fingered species that built the notation.
And this explains the pattern that makes base 10 so powerful in everyday mental arithmetic. Every time you say "ten times", "a hundred times", "a thousand times" — you are quietly using scientific notation's superpower: the exponent is right there in the digits, waiting to be read off.
Related: Exponents and Powers · Drag the Decimal: Scientific to Standard Form · Grain of Rice on a Chessboard · Number Systems