9. A teacher places seven cards, lettered A-G, on
a table. Which cards show irrational
numbers?
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Answer:
Cards C and E
Step-by-step explanation:
Remember that irrational numbers cannot be written as a fraction of two integers:
Is 10 irrational? No, because 10 can be written as a fraction (ex. 10/1, 20/2, etc.)
Is 6/5 irrational? No, because it is a fraction.
Is π irrational? Yes, because it can't be written as a fraction as its digits continue infinitely without repetition.
Is 11/4 irrational? No, because it is a fraction.
Is 8.25635... irrational? Yes, because the ellipsis shows the digits continue infinitely without repetition, otherwise there would be a bar over the digits to show repetition
Is -7 irrational? No, because it can be written as a fraction (ex. -7/1, -14/2, etc.)
Is 6.31(bar) irrational? No, because the bar shows that the digits 3 and 1 repeat.
Therefore, only cards C and E are irrational.