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Six Rational Numbers - Mathematics

by Gagan Bhullar
(Amritsar, Punjab, India.)










































When a number that can be expressed as the quotient of two integers (where integer
in the denominator does not equal zero), that number is a rational number.

find six rational numbers between 3 and 4.

Comments for Six Rational Numbers - Mathematics

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Mar 30, 2012
Six Rational Numbers
by: Staff


Question:

by Gagan Bhullar
(Amritsar, Punjab, India.)


find six rational numbers between 3 and 4.
Answer:


A RATIONAL NUMBER is a number which can be written as a fraction a/b.


Have you ever noticed that the first 5 letters of the word rational spell the word RATIO. We use ratios in everyday life all the time. For example, one person might say a car gets 25 miles per gallon. This is the ratio 25:1, or the fraction 25/1. Another person might say that to mix cookie batter add 1 cup of water for every 3 cups of flour. This is the ratio 1:3, or the fraction 1/3.



>>> Many numbers between 3 and 4 are rational numbers.

Six examples are:

3.1 = 31/10
3.2 = 32/10
3.3 = 33/10
3.4 = 34/10
3.5 = 35/10
3.6 = 36/10

Don’t be concerned about a number such as 19/6 (also between 3 and 4). The decimal equivalent of 19/6 is a repeating decimal. 19/6 = 3.16666666…

Even though the decimal equivalent of 19/6 is a repeating decimal, it is still a rational number because it can be written at a fraction (a/b).


An IRRATIONAL NUMBER, on the other hand cannot be written as a fraction. The decimal value of an irrational number does not have a pattern which repeats itself.

An example of an irrational number which is between 3 and 4 is the square root of 11.

√11 ≈ 3.316624790355399849114932736670686683927088545589353597058682146116484642609....

The numbers do not appear in a pattern which repeats itself, no matter how many decimal places are computed.


One way to remember the difference between the decimal equivalent of a rational number and the decimal equivalent of an irrational number is:

The decimal equivalent of a rational number will terminate, or have a repeating pattern.

The decimal equivalent of an irrational number will never terminate, and it never has a repeating pattern. This is sort of like an irrational person: there is NO PATTERN to their behavior – what they say or do unpredictable.



Thanks for writing.

Staff
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