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Convert the decimal expansion 0.291666... to a fraction

User Dat
by
7.6k points

2 Answers

4 votes
7/24
You could try rounding up to 0.292 first and try guessing it it gets to 73/250 which you could guess into 70/240.
User Steve Miskovetz
by
8.7k points
3 votes

Answer:
(7)/(24)


Explanation:

The given decimal expansion : 0.291666......, where 6 is repeating.

Let
x=0.291666... (1)

First we multiply 10 on the both sides, we get


10x=2.916666...... (2)

Now, subtract (1) from (2), we get


10x-x=2.9166...-0.29166...\\\Rightarrow9x=2.625\\\Rightarrow\ x=(2.625)/(9)=(2625)/(1000)

Simplify it to the lowest fraction, we get


x=(7)/(24)


User Grin
by
8.3k points

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