Calculating the percent increase in the radius of the sun over time.

The Sun has increased in radius by 6% over the past 4.56 billion years. Its present-day radius is 696,000 km. What was its radius 4.56 billion years ago?

The answer is not 654,000 km. Please show your work, and an explanation of how you came to your conclusion would be much appreciated.

The trick to these calculations (where you are given the value AFTER the increase) is to realize that what you NOW have is 6% MORE than the number from which the percentage was calculated.

X = initial radius

X + 6% of X = 696,000
100% of X + 6% of X = 106% of X = 696,000
A percentage is just a fancy way to write a fraction over 100
106% = 106/100

(106/100)X = 696,000
X = 696,000 * 100 / 106 = 656,603.8

Cripes, simple multiplication and division seems to beyond the comprehension of so many people. You just do the following:

696,000 km / 1.06 = 656,603.8 km

Mind you, so many people are brain dead about percentages that many calculators have a percentage button.