document.write( "Question 892211: √51, -55, and -2/15. I need to know which classification of numbvers each are in. Please help!☺ \n" ); document.write( "

Algebra.Com's Answer #540416 by KMST(5328) $\"\"$ $\"About$

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To begin with,
\n" ); document.write( " $\"sqrt%2851%29\"$ , $\"-55\"$ and $\"-2%2F15\"$
\n" ); document.write( "are all real numbers, but maybe you have not been introduced to any other kind of number, so I do not know if \"real\" is part of the expected answer.
\n" ); document.write( "Other than real, I can call those numbers other names:
\n" ); document.write( " $\"sqrt%2851%29\"$ is an irrational number (it cannot be expressed as a fraction, so it is not a rational number)
\n" ); document.write( " $\"-2%2F15\"$ is a rational number (it can be expressed as a fraction),
\n" ); document.write( " $\"-55\"$ is a rational number and can also be called an integer.
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\n" ); document.write( "NOTES:
\n" ); document.write( "1) I do not know if you are expected to say that $\"sqrt%2851%29\"$ is positive, and that $\"-55\"$ and $\"-2%2F15\"$ are negative.
\n" ); document.write( "It seems too obvious, but maybe you are also expected to state the obvious.
\n" ); document.write( "2) Beware of tricks. You may be asked is $\"sqrt%28625%29\"$ is rational, and you may be tempted to say it is irrational because of the square root sign. However, $\"sqrt%28625%29=25\"$ so it is not irrational. You can call it a rational number, an integer, a whole number, and a natural number.
\n" ); document.write( "You could also be asked if $\"49%2F7\"$ is a natural number. SInce $\"49%2F7=7\"$ it is a natural number. It can also be called a whole number, an integer, and a rational number.
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\n" ); document.write( "EXPLANATIONS:
\n" ); document.write( "The real numbers can be classified as rational numbers, or irrational numbers.
\n" ); document.write( "RATIOnal numbers show RATIOs of the simpler numbers we call integers. For example, $\"2%2F3\"$ , $\"-1%2F5\"$ and $\"7%2F1=7\"$ are rational numbers. Rational numbers can also be written as decimals, such as $\"1%2F8=0.125\"$ or $\"1%2F11=%220.0909090909...%22\"$ . (If the decimal has infinite digits, at least there is a repeating pattern, so you can write the exact value as a decimal by showing the repeated pattern followed by dots.
\n" ); document.write( "If a real number is not rational, it is called irrational. $\"sqrt%282%29\"$ and $\"pi\"$ are irrational. Their exact value cannot be written as a fraction or as a decimal. We end up using approximate values, like $\"22%2F7\"$ or $\"3.14\"$ for $\"pi\"$ . People have calculated many digits of $\"pi\"$ , and you could memorize the first few digits, but there is no pattern.
\n" ); document.write( "Some rational numbers can also be called integers, like $\"-3\"$ , $\"0\"$ , and $\"5\"$ .
\n" ); document.write( "Some integers can also be called whole numbers (0, 1, 2, 3, ...).
\n" ); document.write( "Whole numbers other than $\"0\"$ can also be called natural numbers.\r
\n" ); document.write( "\n" ); document.write( "They first real numbers you ever knew were the ones we call \"natural\" numbers: 1, 2, 3, ....
\n" ); document.write( "They come to us very naturally, so it made sense to call them natural numbers.
\n" ); document.write( "The concept of zero is not so natural, but they teach you that early in school.
\n" ); document.write( "After that they teach you fractions, and they tell you that 0, 1, 2, 3, and so on are \"whole\" numbers, to differentiate them from fractions. \n" ); document.write( "

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