decimal expansion

Every real number has at least one infinite decimal expansion.

Also, the decimal expansion of a number is not necessarily unique.

The above approach to decimal expansions, including the proof that 0.999.

The series definition above is a simple way to define the real number named by a decimal expansion.

The decimal expansion of an irrational number continues without repeating.

If 0 appears as a remainder, the decimal expansion terminates.

In the 10-adic numbers, the analogues of decimal expansions run to the left.

This is known as the decimal expansion of pi.

The first sixty significant digits of its decimal expansion are:

After that, a remainder must recur, and then the decimal expansion repeats.

A complementary approach is tailored to the opposite process: for a given real number, define the decimal expansion(s) to name it.

Perhaps the most common development of decimal expansions is to define them as sums of infinite series.

Any rational number can be expressed as a unique decimal expansion ending with recurring decimals.

It is conjectured that 86 is the largest n for which the decimal expansion of 2 contains no 0.

In fact, every real number can be written as the limit of a sequence of rational numbers, e.g. via its decimal expansion.

It is time for bold measures: the sequencing of the entire decimal expansion of pi.

It is greater than π, as can be readily seen in the decimal expansions of these values:

And we know a few more than the first two hundred million digits of the decimal expansion for (Kanada, see Section 3).

It is not even known whether all digits occur infinitely often in the decimal expansions of those constants.

The sequence of digits in the decimal expansion of 1/7 is periodic with period six:

Pi is an irrational number and as such the decimal expansion does not terminate nor does it repeat.

The decimal expansion of an irrational number never repeats or terminates, unlike a rational number.

More generally, the sequence of digits in the decimal expansion of any rational number is eventually periodic (see below).

Calculating digits of the decimal expansion of constants has been a common enterprise for many centuries.

He worked in algebra, trigonometry and geometry; and on the decimal expansion of π.