Properties of Rational versus Irrational Numbers
Not all square roots are irrational, but any square root that can’t be reduced to a form with no radical signs in it is irrational. For example,
Identifying Rational and Irrational Numbers
Identify which of the following are rational numbers and which are irrational numbers.
23.7 can be written as
2.8956 can be written as
Any number whose decimal representation has a finite number of digits is rational, since each decimal place can be expressed as a fraction. For example,
Express the following decimals as fractions.
0.439 can be expressed as
Classify Real Numbers
We can now see how real numbers fall into one of several categories.
If a real number can be expressed as a rational number, it falls into one of two categories. If the denominator of its simplest form is one, then it is an integer. If not, it is a fraction (this term also includes decimals, since they can be written as fractions.)
If the number cannot be expressed as the ratio of two integers (i.e. as a fraction), it is irrational.
Classify the following real numbers.
Irrational (Although it's written as a fraction,
Rational (It simplifies to
Place the following numbers in numerical order, from lowest to highest.
This means that the ordering is:
For questions 1-7, classify the following numbers as an integer, a rational number or an irrational number.
0.25−−−−√ 1.35−−−−√ 20−−√ 25−−√ 100−−−√ π2−−√ 2⋅18−−−−√
- Write 0.6278 as a fraction.
- Place the following numbers in numerical order, from lowest to highest.
- Use the marked points on the number line and identify each proper fraction. License: CC BY-NC 3.0
To view the Review answers, open this PDF file and look for section 2.10.