## 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?

In , Pluto’s distance from the sun is ##3.67xx10^9## miles.

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 ##axx10^n##, where ##1<=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=3.67xx10^(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 ##3.67xx10^9## miles.