jazzybear1543
jazzybear1543 jazzybear1543
  • 27-08-2021
  • Mathematics
contestada

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




745/999

Respuesta :

LammettHash
LammettHash LammettHash
  • 27-08-2021

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.

Answer Link
hawkinsandrew402
hawkinsandrew402 hawkinsandrew402
  • 21-09-2021

Answer:

3 digits

Step-by-step explanation:

Answer Link

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