piclist 2001\06\01\092542a >
www.piclist.com/techref/index.htm?key=brain+burp+rounding
BY : Paul Hutchinson email (remove spam text)

>No it doesn't because 9/9 == 1, not 0.9(recurring)

You missed the point, I was saying that 0.9(repeating) is absolutely equal
to 1. This is a basic principal of mathematics that I think was taught to me
in junior high school.

Here is the algebraic proof:

Given:
x = 0.9(repeating)
Multiply both sides by 10:
10x = 9.9(repeating)
Subtract x from both sides:
10x - x = 9.9(repeating) - x
Substitute value for x on right side:
10x - x = 9.9(repeating) - 0.9(repeating)
Simplify right side:
10x - x = 9
Simplify left side:
9x = 9
Divide both sides by 9:
x = 1
Substitute value for x on left side:
0.9(repeating) = 1

>(and 5/9 is not 0.2 recurring, but I guess that was a typo!)

Yep, a typo should have been 0.5(repeating)

>4.99999999999 (repeating) is not equal to 5.00000000 (repeating), that's
why
>we have different numbers to express it. However, 4.99999999999 (repeating)
>is nearly equal to 5

As above 4.99999999999 (repeating) is exactly equal to 5.

Paul

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