Which of these are irrational and rational?
1. 0.7
2.3.3451 (there is a straight line over the 451)
3. 4 and 5/8s
2007-12-21 05:03:55 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
You seem to have some conflicting answers. The correct answer is that they are all *RATIONAL*.
Rational numbers are those that can be represented as a ratio of integers. But you don't even have to figure that out.
Just know that if a number is a fraction (improper or mixed) it is RATIONAL.
If a number is a decimal (fixed or repeating) it is RATIONAL.
The only numbers that are IRRATIONAL are numbers like π, e, √2, etc. These are numbers that cannot be represented as a decimal. Their decimal representation goes on forever *without ever repeating*.
So, all your answers are RATIONAL.
PROBLEM 1:
0.7 is the same as 7/10
Rational
PROBLEM 2:
.....___
3.3451 is the same as 16709/4995*
Rational
PROBLEM 3:
4 and 5/8s is the same as 37/8
Rational
*To convert to a fraction, this would be the same as 3 + 3/10 + 451/9990. Getting a common denominator 33418/9990 which reduces to 16709/4995.
Again, you don't need to be able to turn it in to an actual fraction, just know that all fractions, all terminating decimals and all decimals that repeat are RATIONAL.
2007-12-21 05:18:25 · answer #1 · answered by Puzzling 7 · 2⤊ 0⤋
All numbers are rational.
3.3451451451...
= (33451 - 33) / 9990
= 33418 / 9990
Since this could be expressed as a ratio of two integers, it is rational. In fact all recurring decimals are rational as they can be expressed as the ratio of integers.
To convert a recurring decimal number as a ratio of integers, follow the following empirical method.
Write all digits dropping the decimal point and writing recurring digits only once and subtract from that digits prior to recurring digits in the numerator. Thus, numerator is 33451 - 33.
In the denominator write as many nine's as there are recurring digits after the decimal point (here three - 4, 5 and 1) followed by as many zeroes as there are non-recurring digits after the decimal point (here, there is one - 3). So denominator here is 9990.
You can verify the result using a calculator.
2007-12-21 05:30:58 · answer #2 · answered by Madhukar 7 · 0⤊ 0⤋
They are all rational. A rational number is one that can be expressed exactly by a fraction, a decimal or a repeating decimal. An irrational number is one that can't, like pi (3.1415926...it never ends or repeats).
Incidentally, that straight line means "repeating". So that number is 3.3451451451451451....
2007-12-21 05:11:00 · answer #3 · answered by Amy F 5 · 1⤊ 0⤋
They're all rational because they can all be described as fractions (except potentially number 2 but that's because I can't think of what .3451451451451451... converts to off the top of my head)
2007-12-21 05:09:05 · answer #4 · answered by tyler_shay4 2 · 0⤊ 1⤋
All of them are rational because each can be written
as a fraction.
2007-12-21 06:24:44 · answer #5 · answered by steiner1745 7 · 0⤊ 0⤋
1. rational: 7/10
2. irrational: repeating
4. rational, already a fraction
2007-12-21 05:10:08 · answer #6 · answered by um... 2 · 0⤊ 4⤋
they all seem irrational
2007-12-21 05:07:54 · answer #7 · answered by I is teh pirate! 2 · 0⤊ 5⤋