Dowqueuestbew1j

2022-01-17

How do you write 3/7 as a terminating or repeating decimal?

rodclassique4r

Expert

There are several formats for indicating a repeating decimal.
(You may want to check the form your instructor likes).
$\frac{3}{7}$ expressed as a decimal fraction is a repeating decimal with a fairly long (7 digit) pattern before repeating (you can verify this by long division.
One form of expressing this repeating pattern is
$\frac{3}{7}=0.428571\left[428571\dots \right]$

macalpinee3

Expert

Just do a manual long division of 3 by 7. After 6 decimals the step reminder is 3 and so the sequence repeats.
(Is manual long division still taught in schools? Or do calculators rule?)
BTW, 1/7 and it’s multiples form a pretty, circular pattern.
$\frac{1}{7}=0.142857$ reccuring
$\frac{2}{7}=0.285714$ recurring
$\frac{3}{7}=0.428571$ reccurring
$\frac{4}{7}=0.571428$ recurring
$\frac{5}{7}=0.714285$ reccurring
$\frac{6}{7}=0.857142$ reccurring.

alenahelenash

Expert

7 is greater as 3 so the first digit of the decimals is zero the remainder is 3 and we add comma to the result and a 0 to the 3, now 7 in 30 is 4 and 2 remainder, $\frac{20}{7}=2R6,\frac{60}{7}=8R4,\frac{40}{7}=5R5,\frac{50}{7}=7R1,\frac{10}{7}=1R3$, so $\frac{3}{7}=0.4285714285714...$