Home > Student activities > National Maths Day > National Maths Day 2014 > Does 0.999… = 1?
Does 0.999… = 1?
Sometimes this seems counter-intuitive. Try using fractions or algebra to show that this is true.
Using fractions:
1/9 = 0.111…
9 x 1/9 = 9 x 0.111…
1 = 0.999…
Using algebra:
x = 0.999…
10x = 9.999…
= 9 + 0.999…
= 9 + x
9x = 9
x = 1
Yes
