how to convert 1e+11 into number?

Question

What will be 1e+11 in number? I know e2 means * 10^2 but i am confused with this above question. What will its value be?

I know how to use exponential function when required in computer calculator but how does it work? I am still studying and our textbooks are not so detailed which gives us the idea how it works. I am using the function but still anyone can explain me in detail about how to convert 1e+11 into number?

Answer 1

You seem to have the right idea.

$$1\text{ e+11}=1 \times 10^{+11}$$

You should know that $10$ raised to any positive integer is a $1$ with that many $0$s behind it. So

$$10^{+11}=100000000000$$

Answer 2

It is just a short notation to make good use of limited display and storage space.

The used string in base 10 representation, called exponential or scientific notation, and the encoded rational number are related by $$ (\underbrace{\pm d.ddd\cdots d}_{\mbox{mantissa }m} \,\,\, \mbox{E}\underbrace{\pm dd\cdots d}_{\mbox{exponent }k})_{10} = m \cdot 10^k $$

with digits $d \in \{ 0, \ldots, 9 \}$, exponential symbol "E" or "e", rational $|m| < 10$ and integer $k$.

The exponent is not to be confused with the exponential function $e^x$.

Also for some problems the "order of magnitude" (i.e. $10^k$) is good enough and the knowledge of all digits not necessary.

In your example the string "1e+11" means the number $1 \cdot 10^{+11} = 10^{11} = 1\underbrace{00000000000}_{11 \, "0" \mbox{symbols}}$

Note that the resulting number is given by a string as well, just a usually more familiar one, the base 10 positional system representation learned in school.

Another example: "0.27e-15" means the number $0.27 \cdot 10^{-15} = 0.\underbrace{000000000000000}_{15 \, "0" \mbox{symbols}}25$