How do you write decimal notation for 5/6?
3 Answers
How I do it in my head is that I start from the fraction
Next, to find
- Divide
#100# by#6# . - Divide by
#100# again.
Since
#100/6 = stackrel("quotient")(overbrace(16)) + stackrel("remainder")(overbrace(4/6)#
#= 16 + 2/3#
#= 16.bar(66)#
Therefore:
#((100)/6)/100 = 1/6 = 0.1bar(66)#
Finally, our answer is:
#color(blue)(5/6) = 6/6 - 1/6#
#= 1 - 0.1bar(66)#
#= color(blue)(0.8bar(33))#
Explanation:
6 cannot be multiplied by any number to give an exact power of 10,
so it is not possible to write an equivalent fraction to get a decimal.
Divide 5 by 6:
It is usually rounded to 2 or 3 decimal places.
Explanation:
Think of 5 as
Observe that
But 5 can be written as
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So now we have
But
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So now we have:
But
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This process repeats indefinitely so we can write this in decimal form as:
Mathematically this is written as
Notice the bar over the last 3 in