Is 9.3 repeating a rational number? - Computers & Internet

All are rational numbers. Any integer is such, and the others as written can be expressed as finite fractions ie

168 / 100
5111 / 1000
9111 /1000

If your notation means that the repeating decimal goes on forever eg

5.111111111111111111111111111111111111111..................

Then it still can be rational, as 46 / 9 is, and 82 / 9

If a number can be expressed as a ratio of two whole numbers then it's rational.
Alternatively, if a number can be expressed in decimal with a finite number of digits or as a repeating decimal then it's rational.

All integers are rational numbers. The easiest way to see that is to write an integer as a fraction with 1 as a denominator; 4=4/1=8/2; 5=5/1.
Any number that can be written as a ratio of two integers numbers is by definition a rational number ( it is a ratio---rational).
Any decimal number with a periodic decimal part can be cast as a fraction, so it is rational.
An irrational number is a number that cannot be written as a fraction.
Examples: PI, sqRT(2), Sqrt(3), SQRT(5), e. There is an infinite number of them.

The product of two rational numbers is another rational number.

Use the words: decimal part, not decimal fractin
Any number whose decimal part is periodic (has a recurring pattern that repeats indefinitely) is equivalent to a rational number, IS a rational number
0.345 345 345 ... =345/999=115/333
In the following screen captures, discard the last digit if it does not belong to a period. It is the effect of rounding up of the calculator



Period is 345


Period is 1

Period is 09

Period is 79


In general, if you have a decimal part of the form 0.d_1 d_2 d_3....d_n d_1 d_2 d_3 ...d_n ... where d_1 is the first digit of the period, d_2 is the 2nd digit of the period, ..., d_n is the n-th digit (and the last one) of the period, then the fraction representation of
0.d_1d_2...d_n d_1d_2... d_n ...=(d_1d_2...d_n)/(99...9) where the number of 9's in the denominator is equal to the number of digits in the period.
Once the fraction is found, one should reduce it to its simplest form.

The opposite of any number (be it integer, rational, or real) is the same number preceded by the negative sign.
Example : the opposite of a is -a (read it a negative a)
opposite of (-b) is -(-b)=b
A rational number is a number that can be written as a fraction. You should note that the set of rational numbers contains the set of all integers .
The opposite of 15/37 is -(15/37) which is equivalent to (-15)/37 and 15/(-37).

The opposite of any number (be it integer, rational, or real) is the same number preceded by the negative sign.
Example : the opposite of a is -a (read it a negative a)
opposite of (-b) is -(-b)=b
A rational number is a number that can be written as a fraction. You should note that the set of rational numbers contains the set of all integers .
The opposite of 15/37 is -(15/37) which is equivalent to (-15)/37 and 15/(-37).

A rational number that can written as the RATIO of two whole numbers.
Examples:
1. Any whole number (-1, +13, -57) because they can be written as -1/1, 13/1 , -57/1.
2.Any number of the form a/b where a and be are integers (whole numbers) 1/3 , 17/(-9), 27/11, -17/9
13.572 572 572... where the sequence 572 (called the period) repeats for ever
-29.0123478478 478...
Numbers such as the square roots of numbers that are not perfect squares are not rational. They are irrational numbers. SQRT(2), SQRT(5), SQRT(6), SQRT(7), SQRT(8), SQRT(10), PI, e the base of natural logarithm, sin(22 degrees), cos(58),

A rational number is a number that can be expressed as the RATIO (see rational) of two integer (whole) numbers. 8 is an integer, and so is 3. The number 8/3 is a RATIO of two integers :it fits the definition of a rational number.

There are an infinite number of rational numbers between any two rational numbers.

Given any two rational numbers, the number midway between them is also rational. By the same logic, the number midway between the smaller of the two original numbers and the midpoint is also rational. And so is the number midway between the first number and the second midpoint. And so is the number midway between the first number and third midpoint... and so on.