Yes, 0.898989... can be written as a fraction. To convert the repeating decimals into a fraction, we can use the "method of differences." Let's assume x = 0.898989... and multiply it by a power of 10 to align the decimal places, as shown below:
10x = 8.989898... (1)
Now, we can subtract equation (1) from x:
10x - x = 8.989898... - 0.898989...
9x = 8.090909...
Now, we subtract equation (1) from equation (2):
9x - (8.989898...) = 8.090909... - (0.898989...)
x = 7.192929...
Now we have two equations:
10x = 8.989898... (1)
x = 7.192929... (2)
Subtracting equation (2) from equation (1) will eliminate the repeating decimals:
10x - x = 8.989898... - 7.192929...
9x = 1.796969...
Now, we can write this as a fraction by dividing both sides by 9:
x = 1.796969... / 9
Simplifying the fraction:
x = 199/99
So, 0.898989... can be written as the fraction 199/99.
0.898989... can be written as a fraction and why?
1 answer