A rational number is a number that can be written as a ratio of two integers a and b, where b is not zero. For example, 4/7 is a rational number, as is 0.37 because it can be written as the fraction 37/100.
Example 1 :
Use a calculator to find the equivalent decimal form of each fraction in the table.
Example 2 :
Now find the corresponding fraction of the decimal equivalents given below. Write the fractions in simplest form.
0.2 = 2/10 = 1/5
0.875 = 875/1000 = 7/8
Example 3 :
What do you notice about the digits after the decimal point in the decimal forms of the fractions? Compare notes with your neighbor and refine your conjecture if necessary.
The digits after the decimal point either repeat or terminate.
Example 4 :
Consider the decimal 0.101001000100001000001…. Do you think this decimal represents a rational number? Why or why not?
Sample answer : No; since the digits after the decimal point do not terminate or repeat, it does not represent a rational number.
Example 5 :
Do you think a negative sign affects whether or not a number is a rational number ? Use -8/5 as an example.
No; -8/5 = -1.6, which is a rational number since the decimal terminates. Rational numbers can be negative.
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