Understanding Real Numbers

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Math › Understanding Real Numbers

Questions 1 - 5
1

Without using a calculator, which of the following is the best estimate for ?

Explanation

We know that and .

Because 90 falls is approximately halfway between 81 and 100, the square root of 90 is approximately halfway between 9 and 10, or 9.5.

2

What number is of ?

Explanation

For percent problems there are verbal cues:

"IS" means equals and "OF" means multiplication.

Then the equation to solve becomes:

3

Place in order from smallest to largest:

Explanation

To place in order, first we must find a common denominator and convert all fractions to that denominator.

have a common denominator of .

have a common denominator of .

have a common denominator of .

Therefore we can use common denominators to make all of the fractions look similar. Then the ordering becomes trivial.

4

Which of the following is NOT a real number?

Explanation

We are looking for a number that is not real.

, , and are irrational numbers, but they are still real.

Then, is equivalent to by the rules of complex numbers. Thus, it is also real.

That leaves us with: which in fact is imaginary (since no real number multiplied by itself yields a negative number) and simplifies to .

5

Which of the following are considered real numbers?

Explanation

Real numbers can be found anywhere on a continuous number line ranging from negative infinity to positive infinity; therefore, all of the numbers are real numbers.

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