How do you make .45555555etc into a fraction? i only know how to do it if it was .4545454545. Can someone explain to me how to do it?
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Try this:
x = 0.4555555...
Now you have a repeating pattern of *1* digit, so multiply both sides by 10^1 (aka 10).
10x = 4.555555...
Now subtract the first equation from the second:
10x = 4.555555...
. - x =-0.455555...
----- .. ----------------
. 9x = 4.1
Multiply both sides by 10 to get rid of the decimal:
90x = 41
Divide both sides by 90:
x = 41/90
Answer:
0.4555555... = 41/90
An alternate way to do this is to think of it as follows:
x = 4/10 + 5/100 + 5/1000 + 5/10000 + ...
Multiply both sides by 10:
10x = 4 + 5/10 + 5/100 + 5/1000 + 5/10000 + ...
Subtract the first equation:
10x - x = 4 + 5/10 - 4/10
9x = 4 + 1/10
90x = 40 + 1
90x = 41
x = 41/90
x = 0.4555555...
Now you have a repeating pattern of *1* digit, so multiply both sides by 10^1 (aka 10).
10x = 4.555555...
Now subtract the first equation from the second:
10x = 4.555555...
. - x =-0.455555...
----- .. ----------------
. 9x = 4.1
Multiply both sides by 10 to get rid of the decimal:
90x = 41
Divide both sides by 90:
x = 41/90
Answer:
0.4555555... = 41/90
An alternate way to do this is to think of it as follows:
x = 4/10 + 5/100 + 5/1000 + 5/10000 + ...
Multiply both sides by 10:
10x = 4 + 5/10 + 5/100 + 5/1000 + 5/10000 + ...
Subtract the first equation:
10x - x = 4 + 5/10 - 4/10
9x = 4 + 1/10
90x = 40 + 1
90x = 41
x = 41/90