###### Asked in Numbers

Numbers

# Name two rational numbers that are close to but smaller than each of the rational numbers given below?

## Answer

###### Wiki User

###### January 11, 2017 11:22PM

There weren't any numbers given below.

## Related Questions

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### Is the set of all rational numbers continuous?

Continuity is a characteristic of functions not of sets.
The set of rational number is infinitely dense. This means that
between any two rational numbers, no matter how close together,
there are infinitely many rational numbers. And then, between any
two of them these is an infinte number of rational numbers, and so
on.
But, in case that gives you any wrong ideas, between any two
rational numbers there is an even higher order of infinity of
irrational numbers. In that respect the number of gaps in the set
of rational numbers (where the irrational numbers would be) is
greater than the cardinality of rational numbers.
Continuity is a characteristic of functions not of sets.
The set of rational number is infinitely dense. This means that
between any two rational numbers, no matter how close together,
there are infinitely many rational numbers. And then, between any
two of them these is an infinte number of rational numbers, and so
on.
But, in case that gives you any wrong ideas, between any two
rational numbers there is an even higher order of infinity of
irrational numbers. In that respect the number of gaps in the set
of rational numbers (where the irrational numbers would be) is
greater than the cardinality of rational numbers.
Continuity is a characteristic of functions not of sets.
The set of rational number is infinitely dense. This means that
between any two rational numbers, no matter how close together,
there are infinitely many rational numbers. And then, between any
two of them these is an infinte number of rational numbers, and so
on.
But, in case that gives you any wrong ideas, between any two
rational numbers there is an even higher order of infinity of
irrational numbers. In that respect the number of gaps in the set
of rational numbers (where the irrational numbers would be) is
greater than the cardinality of rational numbers.
Continuity is a characteristic of functions not of sets.
The set of rational number is infinitely dense. This means that
between any two rational numbers, no matter how close together,
there are infinitely many rational numbers. And then, between any
two of them these is an infinte number of rational numbers, and so
on.
But, in case that gives you any wrong ideas, between any two
rational numbers there is an even higher order of infinity of
irrational numbers. In that respect the number of gaps in the set
of rational numbers (where the irrational numbers would be) is
greater than the cardinality of rational numbers.

###### Asked in Numbers

### Are fractions a rational number?

###### Asked in Math and Arithmetic

### What number matches the number that follows 984339.78?

There is no such number.
The given number is rational and rational numbers are infinitely
dense. Between any two rational numbers - no matter how close
together - there are an infinite number of rational numbers. That
means, whatever number you propose as the "next" number, there are
infinitely many numbers between 984339.78 and your proposed number.
So it cannot be the "next".

###### Asked in Math and Arithmetic

### It is always possible to translate among an equation a table of values and a graph of a relation?

No.
Try to created a table or a graph for the equation:
y = 0 when x is rational,
and
y = 1 when x is irrational for 0 < x < 1.
Remember, between any two rational numbers (no matter how
close), there are infinitely many irrational numbers, and between
any two irrational numbers (no matter how close), there are
infinitely many rational numbers.

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### How many rational numbers can be put between 2 and7?

There are an infinite number of rational numbers between any two
rational numbers. And 2 and 7 are rational numbers. Here's an
example. Take 2 and 7 and find the number halfway between them: (2
+ 7)/2 = 9/2, which is rational. Then you can take 9/2 and 2 and
find a rational number halfway:
2 + 9/2 = 13/2, then divide by 2 = 13/4. No matter how close the
rational numbers become, you can add them together and divide by 2,
and the new number will be rational, and be in between the other
2.

###### Asked in Math and Arithmetic

### How can you use rational number to represent real world problems?

You cannot. The diagonal of a unit square cannot be represented
by a rational number. However, because rational numbers are
infinitely dense, you can get as close to an irrational number as
you like even if you cannot get to it. If this approximation is
adequate than you are able to represent the real world using
rational numbers.

###### Asked in Numbers

### Is there a rational number between any two distinct rational numbers?

Yes. Not only that, but there are an infinite number of
rationals between any two distinct rationals - however close.
We can prove it like this:
Take any three rational numbers, call them A, B and C, where B
is larger than A, and C is any rational number greater than 1:
D = A + (B - A) / C
That gives us another rational number, D, no matter what the
values of the original numbers are.

###### Asked in Numbers

### What is the rational number of 8.3 and 8.26?

8.3 and 8.26 are both rational numbers.
Their sum is 16.56. That's also a rational number.
Their difference is 0.04. That's also a rational number.
Their product is 68.558. That's also a rational number.
Their quotient is close to 0.9952. It can't be completely
written as a decimal,
but it's equivalent to 413/415 and it's a rational number
too.

###### Asked in Math and Arithmetic

### What is closing a rational number under addition And can you close them under subtraction multiplication and division?

Rational numbers are numbers that can be expressed as a fraction
a/b where a and b are both integers and b is not equal to zero. All
integers n are rational numbers because they can be expressed as
the fraction n/1. Rational numbers are closed under addition,
subtraction, multiplication and division by a non-zero
rational.
To be closed under addition, subtraction, multiplication and
division by a non-zero rational means that if you have two rational
numbers, when you add, subtract, multiple or divide them, you will
get another rational number.
For example, take the rationals 1/3 and 4/3. When you add them
together, you get another rational number, 5/3. Same with the other
operations.
1/3 - 4/3 = -1 (remember integers are rational, too)
(1/3) * (4/3) = 4/9
(1/3) / (4/3) = 1/4

###### Asked in Math and Arithmetic, Algebra, Mathematical Analysis

### Why rational numbers are dense then real numbers?

Roughly speaking, rational numbers can form real numbers that's
why they are more densed than real numbers. For example, if A is a
subset of some set X & every point x of X belongs to A then A
is densed in X. Also Cauchy sequence is the best example of it in
which every bumber gets close to each other hence makes a real
number.

###### Asked in Numbers

### What are the two categories of real numbers?

cardinal (1, 2, 3, ...) and ordinal (1st, 2nd, 3rd, ...)
or rational and irrational
A rational number can be expressed as a
fraction
ex: 22/7 is roughly 3.14, very close to pi, but not pi which is
still real but...
Irrational - it cannot be expressed in the form
of a fraction, other irrational numbers: sqrt(2), e.

###### Asked in Math and Arithmetic, Numbers , Irrational Numbers

### Why is the square root of 7 not a rational number?

A rational number is a number that can be written in the form
a/b with a and b relatively prime integers - a and b are whole
numbers with no common factors (eg if a=3 then b can't be
3,6,9,12,etc). Rational numbers have decimal representations that
either terminate (like 3/4=0.75) or are infinitely recurring (like
1/9=0.1111111111... or 5/7=0.714285|714285|714285...).
Irrational numbers (numbers that aren't rational) have infinite
decimals that never repeat (like pi=3.1415926535...,
e=2.7182818284590...). It is possible to prove that unless n is a
square number, the square root of n is irrational - if n can't be
written as m^2 then n^0.5 is irrational.
Since you can't find a and b such that (a/b)^2=7 the square root
of 7 is irrational. It should be noted that you can get as close as
you like to 7^0.5 with rational numbers but you can never reach it
exactly.