3 years ago

How many repeating digits are in the smallest group of repeating digits in the decimal equivalent of the fraction shown?

Mathematics

1 answer:

Anna11 [10]3 years ago

5 0

If x = 745/999, then

999x = 745

1000x - x = 745

This equation tells us that the fractional part of 1000x and x cancel upon subtracting. This means the block of repeating digits must be 3 digits long.

To verify this, suppose we write x = 0.yyy… , where y consists of 3 digits. Then

1000x = y.yyy…

1000x - x = y.yyy… - 0.yyy…

999x = y

x = y/999

which means y = 745.

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