What is the calculator display for 1/3 and is the exact decimal equivalent?
1 answer:
Calculator display = 0.33333333
Is this the exact decimal equivalent? No
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Explanation:
1/3 = 0.33333333.... where the 3's go on forever. The calculator of course can't display infinitely many 3's. At some point, it will stop even if they theoretically go on forever.
We can prove we have this pattern by using long division.
To shorten things, we write to tell the reader "the 3s go on forever". The horizontal bar tells us which digit(s) repeats forever. This is the exact decimal version.
The calculator can only display a finite number of digits, so it is impossible to have the approximate calculator display be the same as the exact decimal equivalent.
Some other examples:
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Both pairs of alternate exterior angles are shown in the diagram below. They are color coded to help show how they pair up and which are congruent.
A thing to notice: choices B, C, and D all have point W as the vertex of the angles. This means that the angles somehow touch or are adjacent in some way due to this shared vertex point. However, alternate exterior angles never touch because parallel lines never do so either. We can rule out choices B,C,D from this reasoning alone. We cannot have both alternate exterior angles on the same exterior side of the train tracks. Both sides must be accounted for.