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.
Solution :
Example 2 :
Now find the corresponding fraction of the decimal equivalents given below. Write the fractions in simplest form.
0.2, 0.875
Solution :
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.
Solution :
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?
Solution :
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.
Solution :
No; -8/5 = -1.6, which is a rational number since the decimal terminates. Rational numbers can be negative.
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