**Problem**

**Introduction**

A student
asked the above question on Facebook. This
article explains

*recurring decimals*, which is part of the topic on real numbers in the Singapore Secondary 1 Mathematics syllabus.
By the way,
I do not believe that Asians are inherently better at mathematics. A few students
are working over Christmas to prepare for the next years’ work. Here we go!

**Notation**

Personally, I prefer the horizontal bar notation which
is what I learned during my time as a student, but nowadays in Singapore
schools, we tend to use the dot notation.
There is no right or wrong about this, but it is just a matter of
convention. When in Rome , do as Romans do.

**Coversion to a fraction**

**Concluding Remarks**

A

**ratio**nal number is a number that can be expressed as a**ratio**or fraction*/*^{p}*where*_{q}*p*and*q*are integers with*q*¹ 0. The fraction can be proper or improper. Since any recurring decimal can be converted to a*fraction*,
every (infinitely)
is a recurring decimal.rational
number |

Now,

every
is
also a finitely terminating decimal.rational number |

For example, 0.171 =

^{171}/_{1000}. The numbers that cannot be converted to fractions are called ir**ratio**nal numbers. How do these numbers look like?
The
are exactly the
numbers with irrational numbers (infinite) and non-terminating decimal
expansions.non-recurring |

Some examples of irrational numbers are

e = 2.718 281 828 459 045 235 360 287 471 352 662 497 757 ¼

*p*= 3.141 592 653 589 793 238 462 643 383 279 502 884 197 ¼e = 2.718 281 828 459 045 235 360 287 471 352 662 497 757 ¼

Ö2 = 1.414
213 562 373 095 048 801 688 724 209 698 078 570 ¼

The decimal digits of irrational numbers never end,
but they do not have any repeating pattern. There are actually much “more”
irrational numbers than rational numbers, but this is a fact that is
technically profound, way beyond the secondary syllabus. The interested reader can refer to this article.**Suitable Levels**

*****Lower Secondary Mathematics (Sec 1 ~ Grade 7)

* revision for GCE ‘O’
Level “Elementary” Mathematics (revision)

* other syllabuses that involve recurring
decimals

* any independent learner who is interested

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