On average, the planet Pluto's distance from the sun is about 3,670,000,000 miles. How do you express this distance in scientific notation?

Nov 17, 2016

In scientific notation, Pluto's distance from the sun is $3.67 \times {10}^{9}$ miles.

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.

Her, we intend to write the large number $3 , 670 , 000 , 000$ in scientific notation. To write $3 , 670 , 000 , 000$ in scientific notation, as we have a whole number, decimal is at the end the number (as $3$ is in fact $3.0$) and we will have to move the decimal point nine points to left, which literally means dividing the large number by ${10}^{9}$.

Hence in scientific notation $3 , 670 , 000 , 000 = 3.67 \times {10}^{9}$ (note that as we have moved decimal nine points to the left, to compensate, we are multiplying by ${10}^{9}$.

Hence, in scientific notation, Pluto's distance from the sun is $3.67 \times {10}^{9}$ miles.