High School Math : Understanding Real Numbers

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Understanding Real Numbers

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

Possible Answers:

Correct answer:

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.

Example Question #2 : Understanding Real Numbers

Place in order from smallest to largest:

Possible Answers:

 

Correct answer:

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.

Example Question #3 : Understanding Real Numbers

What number is of ?

Possible Answers:

Correct answer:

Explanation:

For percent problems there are verbal cues:

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

Then the equation to solve becomes:

Example Question #4 : Understanding Real Numbers

Which of the following is NOT a real number? 

Possible Answers:

Correct answer:

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 

Example Question #5 : Understanding Real Numbers

Which of the following are considered real numbers? 

Possible Answers:

Correct answer:

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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