Question

5 interesting mathematical facts about our earth. Need answer immediately Fast!!!!!!!!!! Please help.

Answer 1

Answer:

0.999... = 1

How can 1 equal 0.999? Well, it does, and we can prove that in two different ways.

Proof 1:

If N = 0.999, then 10N = 9.99.

10N - N is therefore 9.99 - 0.999 therefore 9N = 9 therefore N =1

Proof 2:

If N = 0.999 then N divided by 9 is 0.111

Express this as the equation:

0.111 = 1/9

Multiplying both sides by 9 produces:

0.999 = 1

What's going on here? In two words, 'decimal expansion'. 0.999 really represents 0.999999999 and on ad infinitum with each place to the right of the decimal point representing a further negative power of 10.

So the decimal expansion 0.9999... actually represents the sum 9/10 + 9/100 + 9/1000. Adding a further place of decimals (0.9999) would add just 9/10000 and so on into infinity until the two values are so close as to be indivisible.