Rational and irrational numbers step by step

Is every rational number an integer?

The definition of a rational number: Can be expressed, exactly, as the ratio of two integers. An integer is a whole number that can be expressed as positive, negative, or zero. Therefore, only those rational numbers that can be expressed, exactly, as the ratio of n/1, where n is a positive or negative whole number are integers. Zero, a special case, is not considered positive or negative.

Is zero a rational or irrational number?

1. 0 is an integer and all integers are rational numbers. 2. Rational Number - A number (a) is said to be rational if a=p/q for some p belonging to integer and q belonging to integer - {0} We can write 0 as 0/1, 0/2, 0/3 where 0 belongs to Z and 1,2,3 or any number belongs to Z - {0}, where Z is set of integers.

What are the rational numbers between 0 and 1?

A number which can be written in the form of p/q is a rational number. Where p and q are integers but q should not be zero. For rational number between 0 and 1 p<q. So there are infinite rational number between 0 and1. eg. 1/2,1/3,1/4..... Even zero is rational number.

Are all fractions rational numbers? Why?

A rational number is a fraction p/q p/q where pp and qq are integers and q≠0q≠0. So all rationals are fractions, and all fractions having rational numerator and denominator are rational.

What are the three rational numbers between -0.56 and -0.57?

Add your two numbers together . What did you get? I got -1.13 . Divide that number by two . What did you get ? I got -.565 . This is a rational number that is between the two numbers you added together. Add two of your numbers together , two neighboring numbers . Divide that number by two . You got a rational number that is between the two numbers that you just added together . Repeat steps three and four , you now have three rational numbers that are between your two numbers. Repeat as often as you wish. There are, of course, many other methods. Write down the number that has the smaller absolute value ... -.56 write down the month , day, and year of your birth in number form, without any punctuation , for example , -.5609261951 this is a rational number between -.56 and -.57 repeat step two as often as you like. How many different numbers can you come up with? Please note, you could keep writing a longer and longer and longer number , and end up with ...>>> -.56 ( your birthday )( your mom's birthday )( your dad's birthday )( and so on ) There are of course many other methods you could use. Be creative .

Can negative numbers rational or irrational?

Answer: Yes. Take any negative integer for example, -3 = can be expressed as = −31−31 -1 = can be expressed as = −11−11 -99999 = can be expressed as = −999991

Is 0.6 a rational number?

Any number, which can be expressed as a homogenous fraction is eligible to be rational. As 0.6 can be expressed as 6/10=>3/5 ,so is rational.

Can negative numbers be irrational?

Let's identify a couple of irrational numbers that students see quite often. ππ comes to mind. So does the square root of non-perfect squares like 2-√2, 3-√3, 5-√5, 13−−√13, etc. (Why are the square root of non-perfect squares irrational? That's a whole other story.) Now, if you look at a number line, these irrational numbers that I just mentioned have their opposites located on the left-hand side of where zero is. That's where all the negative numbers are located- even the irrational ones! They would be -ππ, -2-√2, -3-√3, -5-√5, -13−−√13, etc. So yes, negative numbers can be irrational.

How can 7−43-√−−−−−−−√7−43 be simplified?

The trick here is to write the expression under the square root as a square of something. In fact, you can write (let's suppose that a>ba>b): 7−43-√=(a−b)2=a2+b2−2ab7−43=(a−b)2=a2+b2−2ab By identification, we have: 7=a2+b27=a2+b2 and 23-√=ab23=ab Trying a=2a=2 and b=3-√b=3 works. Thus: 7−43-√−−−−−−−√=(2−3-√)2−−−−−−−−√=2−3-√7−43=(2−3)2=2−3.

How can I find the rational numbers between -1 & 0?

There are infinite rational numbers between -1 and 0 Take the following form: -0. and append any real number you can think of with finite number of digits.(eg. -0.323, -0.895217294123, -0.321482624184721924812492192041, etc) Thereafter, keep adding these numbers to your list of rational numbers between -1 & 0.