What is $10^{40}$ as a number?

Question

What is $10^{40}$?

Every time I google this question I get $1\mathrm{e}\!+\!40$ but I don’t understand this so what is it as a number?

Answer 1

I'm assuming you know that for any real number $a$ and whole number $n$, $a^n$ is the product of $n$ factors of $a$: $$ a^n = \underbrace{a \cdot a \cdots a}_{\text{$n$ factors}} $$ So $10^{40}$ is the product of forty tens, all in a row.

In our base-ten system, multiplying by ten has the effect of adding a zero to the end of the number. So $10^{40} = 10 \times 10^{39}$ is $10$ followed by $39$ zeroes. In other words, $1$ followed by forty zeroes.

This is useful in scientific notation. It's a way to conveniently express very large or very small numbers without writing a lot of zeroes. For instance, the number $1234500000$ can be written as $1.2345 \times 10^9$. A calculator or computer expresses scientific notation with the letter e for “exponent” (of the base 10). So $1.2345 \times 10^9$ gets printed as 1.2345e+9.

Answer 2

This is $$10^{40}=10000000000000000000000000000000000000000$$

Answer 3

... or ten thousand trillion trillion trillion (where 1 trillion = $10^{12}$) or, even shorter, ten duodecillion.

Answer 4

OK, $10^{39}$ is called one Duodecillion

hence:

$10^{40}$ is ten Duodecillion