How do you write 1/6 as a decimal?

2 Answers
G_Ozdilek
Mar 12, 2018

1/6 is 0.166666666666666666666. And it is 16.666666666666%

Explanation:

#1/6 = 0.1666666666666666666666666666666#

In percentage form:

#100times0.16666666666666666666666666666 = 16.66666666666666666666666666%#

Alan N.
Mar 12, 2018

#0.1dot6#

Explanation:

#1/6 = 0.1666666666....#

This is an infinite decimal because the string of 6's repeat indefinitely.

For practical purposes this is often rounded off - E.g. #0.167# but it is important to note that this is only an approximation of #1/6#.

To overcome this, we can use the dot or bar notation to indicate that a decimal digit (dot) or sequence of decimal digits (bar) repeat indefinitely.

Thus, in this case, as the #6# recurs indefinitely we can notate its first occurrence as #dot6#

Hence, #1/6 = 0.1dot6#

[NB: It is worth noting that repeating decimals should not be confused with irrational numbers. In fact, it can be shown that all repeating decimals are rational (like #1/6#). Whereas, irrational numbers have infinite decimals that do not repeat.]

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