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To write 0.6666 as a fraction, we first note that the number has a repeating decimal pattern. To convert this to a fraction, we can set x = 0.6666 and subtract the non-repeating part of the decimal, which is 0.6. This gives us x - 0.6 = 0.06666. Simplifying this equation, we get x = 2/3. Therefore, 0.6666 is equivalent to the fraction 2/3.
If you mean 0.6666 as a terminating decimal, write it without the decimal point (and leading zero) over 1 followed by the same number of zeros as digits in the number and reduce:
0.6666 = 6666/10000
= 3333/5000
If you mean the recurring decimal 0.6666... where the 6 repeats forever, write the digits that repeat over the same number of nines as the number of digits that repeat and reduce:
0.6666.... = 6/9
= 2/3
If you have a number where some digits do not repeat, and then some do, eg 0.8333... then use both of the above methods together (with a suitable multiplier of the repeating fraction):
0.8333... = 0.8 + 0.0333...
= 0.8 + 1/10 x 0.333...
= 8/10 + 1/10 x 3/9
= 24/30 + 1/30
= 25/30
= 5/6
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