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Real numbers and irrational estimates
Real numbers and irrational estimates
Example 1
Which number is irrational?
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Answer: √2
- √2 cannot be expressed as a ratio of integers. A terminating decimal, a fraction and √49=7 are rational.
Example 2
Which statement about π is correct?
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Answer: π is irrational; 3.14 is a rational approximation
- π has a non-terminating, non-recurring decimal expansion. The finite decimal 3.14 is only an approximation.
Example 3
√157 lies between which two consecutive integers? Enter the smaller integer.
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Answer: 12
- 122=144<157<169=132, so the smaller bounding integer is 12.
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