# How do you write 3,610,000 in scientific form?

Sep 23, 2016

$3 , 610 , 000 = 3.61 \times {10}^{7}$

#### Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of $10$.

Note that moving decimal $p$ digits to right is equivalent to multiplying by ${10}^{p}$ and moving decimal $q$ digits to left is equivalent to dividing by ${10}^{q}$.

Hence, we should either divide the number by ${10}^{p}$ i.e. multiply by ${10}^{- p}$ (if moving decimal to right) or multiply the number by ${10}^{q}$ (if moving decimal to left).

In other words, it is written as $a \times {10}^{n}$, where $1 \le a < 10$ and $n$ is an integer.

To write $3 , 610 , 000$ in scientific notation, we will have to move the decimal point six points to left, which literally means dividing by ${10}^{7}$.

Hence in scientific notation $3 , 610 , 000 = 3.61 \times {10}^{7}$ (note that as we have moved decimal one point to right we are multiplying by ${10}^{7}$ to compensate for division by ${10}^{7}$..

Oct 3, 2016

$3.61 \times {10}^{6}$

#### Explanation:

Taken it 1 step at a time so you can see what is happening.

The multiply by 10's converts the number back to its original state of 3610000

$\textcolor{b l u e}{3610000}$
$\textcolor{b l u e}{361000} .0 \times 10$
$\textcolor{b l u e}{36100} .00 \times 10 \times 10$
$\textcolor{b l u e}{3610} .000 \times 10 \times 10 \times 10$
$\textcolor{b l u e}{361} .0000 \times 10 \times 10 \times 10 \times 10$
$\textcolor{b l u e}{36} .10000 \times 10 \times 10 \times 10 \times 10 \times 10$
$\textcolor{b l u e}{3} .610000 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \textcolor{red}{\leftarrow \text{ This one}}$

Write as: $3.61 \times {10}^{6} \text{ "->" }$This has exactly the same value as $\text{ }$3,610,000