Order of Real Numbers

Key Questions

• How do you classify real numbers?

  Answer:

  Irrational and rational numbers
  Rational numbers: integers, whole numbers, counting/natural numbers

  Explanation:

  Real numbers are either irrational or rational. Rational numbers can be written as fractions (using two integers, such as `4/5` or `-6/3`). Terminating decimals and repeating decimals are examples of rational numbers.

  Rational numbers: `3, -9, 12, -777, 0.3bar3, 12/7, 0.46, 0.16bar6`

  Irrational numbers: `sqrt2, sqrt3, sqrt5, 2sqrt3, -sqrt13, pi`

  There are several different groups of rational numbers. There are integers, whole numbers, and counting/natural numbers. Integers do not have decimals. They can be positive or negative.

  Integers: `6, 16, -72, 89, 23, -1, 0`

  Whole numbers are all non-negative integers. Examples include `16, 0, 23, 45559`.

  Natural/counting numbers are all positive integers. (We don't start counting from zero).

  Counting numbers: `1, 2, 3, 4, 5...`

  Serena D. · 1 · Apr 16 2018
• How do you compare real numbers?

  You can either compare their decimal representations or compute the difference to see if it is positive or negative.

  ---

  Example 1

  `pi=3.14...`

  `2sqrt(3)=3.46...`

  Hence, `pi < 2sqrt{3}`.

  ---

  Example 2

  `2sqrt(2)-e=0.11...>0`

  Hence, `2sqrt{2} > e`

  ---

  I hope that this was helpful.

  Wataru · 2 · Nov 9 2014
• What are Real Numbers?

  You can think of a real number as a number that has a decimal representation including the ones having infinitely many digits.

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  I hope that this was helpful.

  Wataru · 1 · Oct 26 2014

• What are Real Numbers?
• What does it mean to order a set of real numbers?
• What are the different types of rational numbers?
• What kind of rational number is 0?
• How do you classify real numbers?
• How do you compare real numbers?
• What are examples of non real numbers?
• How would you categorize the number `\frac{\sqrt{36}}{9}`?
• Which number is larger between `\frac{\pi}{15}` and `\frac{\sqrt{3}}{\sqrt{75}}`?
• How would you classify each of the following numbers: `\frac{\sqrt{12}}{2}, 1.5\cdot \sqrt{3}, \frac{3}{2}, \frac{2\sqrt{5}}{\sqrt{20}}`?
• How would you order the number from least to greatest: `\frac{\sqrt{6}}{2}, \frac{61}{50}, \sqrt{1.5}, \frac{16}{13}`?
• How do you find a "REAL NUMBER" between pairs of numbers 3 1/3 and 3 2/3?
• What is a real number, a whole number, an integer, a rational number, and an irrational number?
• What is NOT a real number?
• Is -12 an integer, rational, or real number?
• Which real number subset do the following real numbers belong: 1/4, 2/9, 7.5, 10.2? integers natural numbers irrational numbers rational numbers tahaankkksss! <3?
• Is the real number `sqrt(1.21)` rational or irrational?
• What is a real number and can you explain why the inequality x<2 or x>1 has every real number as a solution?
• Between any 2 real numbers's "a" and "b" there is always another real number but how can you find the other number?
• Is 1.3 a real number?
• Can real numbers be negative?
• Is every rational number an integer?
• How do you classify each number as natural, whole, integer, irrational, or real: 12/3, 15, pi/2, -891, 3.3?
• How do you round both of these decimals to the nearest integer: 623.425 and 702.725? thank u so much!?
• Are integers the same as whole numbers?
• Is the square root of 25 an integer because it equals 5 which is an integer?
• How can I tell a rational and irrational number apart?
• Can you give me examples of real numbers?
• Can you give me examples of natural numbers?
• Why is 0/0 undefined?
• Is 2.01 a rational, integer, natural, irrational?
• Is a fraction a real number, rational number, irrational number ?
• Is `-sqrt36` a rational or irrational number?
• Is `-sqrt54` a rational or irrational number?
• Is `sqrt400` a rational or irrational number?
• Is `3pi` a rational, irrational number, natural, whole or integer?
• Is `pi` a rational, irrational number, natural, whole or integer?
• Is `0.99999999` a rational, irrational number, natural, whole or integer?
• Is `0.323232...` a rational, irrational number, natural, whole or integer?
• Is `1/3` a rational, irrational number, natural, whole or integer?
• Is `6/7` a rational, irrational number, natural, whole or integer?
• Is `5/7` a rational, irrational number, natural, whole or integer?
• Is `2/3` a rational, irrational number, natural, whole or integer?
• How do you find a "REAL NUMBER" between pairs of numbers 3 1/3 and 3 2/3?
• Is -3 a rational, irrational, natural, whole, integer or real number?
• Is `3/4` a rational, irrational, natural, whole, integer or real number?
• Is `5` a rational, irrational, natural, whole, integer or real number?
• Is 0.4444... a rational, irrational, natural, whole, integer or real number?
• Is 0 a rational, irrational, natural, whole, integer or real number?
• Is -10 a rational, irrational, natural, whole, integer or real number?
• Is 1/4 a rational, irrational, natural, whole, integer or real number?
• Is `sqrt9` a rational, irrational, natural, whole, integer or real number?
• Is `sqrt7` a rational, irrational, natural, whole, integer or real number?
• Is 2.2360679774998... a rational, irrational, natural, whole, integer or real number?
• Is 2/9 a rational, irrational, natural, whole, integer or real number?
• Is 7.5 a rational, irrational, natural, whole, integer or real number?
• Is 10.2 a rational, irrational, natural, whole, integer or real number?
• How can you write 1.2244444444444444.... as a fraction?
• Is -2 real number, rational number, whole number, Integer, Irrational number?
• Is 4.2 real number, rational number, whole number, Integer, Irrational number?
• Is `sqrt21` real number, rational number, whole number, Integer, Irrational number?
• Is 0.8 real number, rational number, whole number, Integer, Irrational number?
• Is `- 3.96213` real number, rational number, whole number, Integer, Irrational number?
• Is 0.8 repeating a real number, rational number, whole number, Integer, Irrational number?
• Question #8eda1
• How does `0.99999....=1`?
• Question #7a1a0
• Question #3f65b
• How do you simplify `( -64 + 4*4 ) ^ 3`?
• How do you order the following from least to greatest `-11/5, -pi, -2.98, -sqrt7`?
• How do you order the following from least to greatest `4.5, 3 5/6, sqrt16, 8/3, 2pi`?
• How do you order the following from least to greatest `sqrt(7/2), sqrt11, -sqrt16, -3.3, -sqrt36`?
• How do you order the following from least to greatest `sqrt4, 1.8, -sqrt10, -sqrt(36/9), 5`?
• How do you order the following from least to greatest `sqrt3, 1.23, 1.5, 1.58, 0`?
• How do you order the following from least to greatest `5/4, 4/5, 0.45, 0.545`?
• How do you order the following from least to greatest `2.75, 2sqrt3, 15/4, 11.6`?
• How do you order the following from least to greatest `4 4/5, sqrt19, -sqrt5, -21, sqrt5`?
• How do you order the following from least to greatest `-sqrt49, -sqrt7, 0, -sqrt51, -6.8`?
• How do you order the following from least to greatest `sqrt14, sqrt(49/36), 3 3/5, 3`?
• How do you order the following from least to greatest `sqrt6, 1.7, 9/5, 2`?
• How do you order the following from least to greatest `-sqrt8, -3.1, sqrt15, (-2)^2, -sqrt11`?
• How do you order the following from least to greatest `0.19, 0.09, 0.9, 1, 0`?
• How do you order the following from least to greatest `1.9, 2sqrt(11/4), sqrt5, 3 5/6`?
• How do you order the following from least to greatest `sqrt(1/2), sqrt(1/3), sqrt(2/3), sqrt(3/4)`?
• How do you order the following from least to greatest `-sqrt(5/6), -sqrt(19/7), -sqrt(11/4), -sqrt(4/5)`?
• How do you order the following from least to greatest `sqrt2, 2.1, -sqrt4, 0, -5/2`?
• How do you order the following from least to greatest `7/2, sqrt11, -sqrt16, -3.3, -sqrt5`?
• How do you order the following from least to greatest `4.8, sqrt17, -sqrt8, -4.2, sqrt25`?
• How do you order the following from least to greatest `-sqrt1, 0.1, sqrt13, -3/5, sqrt6`?
• How do you order the following from least to greatest `-sqrt5, pi/2, pi/3, 4 5/8, sqrt18`?
• How do you order the following from least to greatest `3/7, sqrt1/sqrt2, 0.46, sqrt5/6`?
• How do you order the following from least to greatest `-11/5, -pi, -2.98, -sqrt7`?
• How do you order the following from least to greatest without a calculator `2/3, -0.75, sqrt8, -9/5, pi/3, 2 1/4`?
• How do you order the following from least to greatest without a calculator `sqrt102, 10, 3pi, sqrt99, 1.1times10^1, 9.099`?
• How do you order the following from least to greatest without a calculator `-sqrt10, -10/3, -3, -2.95, -3 1/4, -3.5 times 10^0`?
• How do you order the following from least to greatest without a calculator `-5, -sqrt24, -26/5, -5.5, -2pi, -4 3/4`?
• How do you order the following from least to greatest without a calculator `8.1 times 10^3, 2.1times10^5, 7.25times10^3, 1.05times10^4, 1.75times10^4`?
• How do you order the following from least to greatest without a calculator `0, -sqrt2, sqrt5, 13/4`?
• How do you order the following from least to greatest without a calculator `3, sqrt10, 3/4, -1.5`?
• How do you order the following from least to greatest without a calculator `2, -3/7, 0.75, -3/2`?
• Which `3` digit number is both a square and a cube?
• Question #515a7
• What numbers are between #4.03 and 4 1/5%?
• Is 0.354355435554 rational or irrational or integer?
• Solve `{(y^2+x=12),(x^2+y=12):}` ?
• Question #f4bbe
• What practical examples are there of uses of the real number line in everyday life?
• Are octonions numbers?
• How you solve this? Solve in `ZZ_6` equation:`hat(x)^3=hatx`
• Question #5a5b8
• How do you simplify `\frac { 5( 1- 4) } { 1- 8}`?