Kaitlin Clark's Irrational Quizizz Competition

How would you classify the following number?

π

• Rational

• Irrational

Answer explanation

Pi is the most famous irrational number. It is a very important constant in mathematics and science. So important that Google decided to use the resources to calculate Pi to a precision of 100 trillion digits.

Tags

CCSS.8.NS.A.1

• Rational

• Irrational

Answer explanation

By definition, a rational number is one that can be represented as a fraction with integer numerator and denominator.

• Rational

• Irrational

Answer explanation

Evaluate this radical (do the math) using Desmos. Pretty definitive ... the decimal version will not terminate.

• Rational

• Irrational

Answer explanation

This evaluates to -19, an integer and rational number. Remember that both rational and irrational numbers can be either positive or negative.

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

This time you had multiple options to consider. Remember that all numbers we will work with this year are Real numbers. Every number is also either a rational number, or an irrational number (but not both).

How would you classify the following number? Check ALL answers/categories that apply.

0.38172

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

When a decimal number terminates, even with several digits to the right of the decimal point, the number is rational.

Remember that Desmos doesn't include the ... after irrational numbers. We wish it did.

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

The line over the last two digits tells us that the 34 repeats forever. This decimal number does not terminate, but we learned that repeating decimals can always be converted into a fraction (ration) ... which is why this one is rational.

How would you classify the following number? Check ALL answers/categories that apply.

0.44...

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

We have seen this before. It is a trick. The 0.44 appears to be repeating 4's, but the ... afterwards tells us that the number never terminates. We can't assume that this is a repeating decimal...we have no idea what even the third digit is.

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

This fraction simplifies to the number 2 (the pi's cancel).

• Real

• Imaginary

• Rational

• Irrational

Answer explanation

Imaginary number ... 5 times the square root of -1. NO FAIR Mr. ROSE!!! Yes, I know. I told you that all the numbers we will deal with are real. I also told you about imaginary numbers...we won't see i again this year.

Imaginary numbers are neither rational or irrational.