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?

1 Answer
Nov 17, 2016

In scientific notation, Pluto's distance from the sun is #3.67xx10^9# 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 #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.