is 0.375932667 a rational or irrational number?

Question

is 0.375932667 a rational or irrational number?



oh and is 0 a rational or irrational number? how do i tell? is it a "real number" too?

Answer 1

See, first let us see what exactly is meant by an irrational no. I rrational nos. are non-terminating non-repeating numbers such as 1.123456789637631...... Numbers such as 0.33333333..... are rational and not irrational.

Rational numbers are those numbers which can be expressed in the form of p/q where q not equal to 0. 0.33333333.... is rational since it can expressed as 1/3 .

According to ur ques., i think 0.375932667 is a rational numbr since it can be represented as 375932667/1000000000.

But if it was 0.375932667..... that wud become non-terminating non-repeating no. thus it wud be an irrational number.


Also, 0 is a rational as well as a real number.

Answer 2

√2 walks into a bar and orders a drink. The bartender brings him his drink and asks him how he's doing. √2 looks at the bar tender and says in a perfectly calm and thought through voice, "you know, I can be written as a ratio of integers." The bartender quickly takes the drink away from √2. √2, being confused, asks "hey, what gives?" The bartender responds, "you have obviously had too much to drink, you are being irrational."

And integer is any whole number, positive or negative: {. . ., -3, -2, -1, 0, 1, 2, 3, . . .}

A rational number, by definition is a number that CAN (not always is though) be written as a ratio of integers (where the bottom is not 0). Any terminating decimal number (terminating meaning only finitely many digits), such as the one you wrote, can easily be written this way because the number a.x_1x_2x_3 . . .x_n (where a is an integer, and the x_i's are digits) =ax_1x_2 . . .x_n/(10^n) and thus is a ratio of integers.

It actually can be shown that any decimal number that has a repeating sequence, such as 0.47182828282828 . . ., can be written as a ratio of integers, and is thus a rational number. That takes a bit more work though.

All integers are rational numbers, because for any integer a, a=a/1 and thus can be written as a ratio of integers.

Therefore, since 0 is an integer, it is a rational number

All rational numbers are real numbers, so 0 is also real.

Answer 3

All rational numbers are real numbers. A rational number is one that can be written as a fraction p/q with both p and q whole numbers. So, 0=0/1 is rational. Now,
.375932667=375932667/1000000000,
so it is a rational number also.
In fact, any number that has a finite decimal expansion is rational. But some numbers like
1/3=.333333....
with infinite expansions are also. The key is that 1/3 has a repeating expansion. Similarly,
1/7=.142857142857142857....
repeats 142857 over and over again.
An irrational number will be one that has an infinite decimal expansion that never repeats. For example,
.101001000100001000001....
where the number of zeros keeps going up will be irrational.

Answer 4

I believe the former is a rational number...

And 0 is rational too...As well as a real number...

A real number is all numerals ex. -3, -2, -1, 0 ,1, 2, 3 ......

By the way, I am not sure about the first one...

Answer 5

If you can write out a number as a decimal, without using a repetition bar or ellipses (i.e., 0.333333...), then it's always a rational number. 0.625 can be written as 625/1000, satisfying the requirement that the number can be expressed as a ratio of two integers. You can simplify it from there, but you don't need to to know that it's rational. Any number that cannot be written out this way, like pi (3.141592..) or e (2.718281...), or which cannot be simplified without removing radical signs (like sqrt(3)) is an irrational number.

Answer 6

You really need to understand your number systems,
Let me give you a brief overview
Natural Numbers: 1,2,3,4,5,................
Whole Numbers: all natural numbers and 0
Integers: ................,-3,-2,-1,0,1,2,3,................
rational numbers: all numbers which can be writtten as a fraction p/q(q not equal to zero) p,q are integers, includes the integers
irrational numbers: all numbers which are not rational
real numbers:all rational and irrational numbers
on a different level we also have the Complex numbers but do not worry too much about them just yet.
now for you specific case:
0.375blah blah blah , as long as the number of digits after the decimal point is finite(hope you understand the concept of finiteness) the number is RATIONAL.
so 0 is also rational(zero digits after the decimal point)
And EVERY rational number is obviously a real number.
hope i have answered your question

Answer 7

0.375932667 if it is only upto there then it is a rational number because it's decimal was terminated...
but if 0.375932667......... so on and so forth which doesn't end then it is an irrational number because it's decimal goes on and on where it doesn't terminate...

0 is neither rational nor irrational and not a real number....

Answer 8

It is a rational number.
The numbers with finite decimals are rational.
The numbers with repeated decimals are rational.
But, the decimal numbers with infinite decimals with a regular repitition are NOT rational, they are irrational.
Rational numbers and Irrational numbers combined together are called Real numbers. So, the number you have given is real.

Answer 9

0.375932667 is a rational number since it can be written as a fraction:

375932667/1000000000

All rational numbers are real numbers.

Answer 10

as the number u have typed is a terminating number that is terminating at 7 ,its an rational number
o is rational and a real number