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irinina [24]
3 years ago
6

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 <em>x</em> = 745/999, then

999<em>x</em> = 745

1000<em>x</em> - <em>x</em> = 745

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

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

1000<em>x</em> = <em>y</em>.<em>yyy</em>…

1000<em>x</em> - <em>x</em> = <em>y</em>.<em>yyy</em>… - 0.<em>yyy</em>…

999<em>x</em> = <em>y</em>

<em>x</em> = <em>y</em>/999

which means <em>y</em> = 745.

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Step-by-step explanation:

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