Common Core Cumulative Standards Review
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Consider rational numbers other than 0.
D
When written as decimals, these numbers either repeat or terminate. Furthermore, multiples of rational numbers are also rational numbers.
| a/b | Decimal Form | Multiple | Product |
|---|---|---|---|
| 1/3 | 0.333333... | 1/3* 7 | 2.333333... |
| 6/1 | 6.0 | 6/1* 7 | 42 |
| 27/4 | 6.75 | 27/4* 7 | 47.25 |
However, an irrational number is a never-ending, non-repeating decimal number. It cannot be expressed as ab, where a and b are rational numbers and b≠ 0. Multiples of irrational numbers are also irrational. Let's look at π and sqrt()3 as examples.
| a/b | Decimal Form | Multiple | Product |
|---|---|---|---|
| π | 3.141592... | π* 7 | 21.991148... |
| sqrt()3 | 1.732050... | sqrt()3* 7 | 12.124355... |
The product of an irrational number and a nonzero rational number is always an irrational number. This corresponds to option D, but only if the rational number is nonzero.