Understanding Rational and Irrational Numbers

What is a rational number?

• A number that cannot be expressed as a fraction

• A number that can be expressed as a fraction of two whole numbers

• A number that is always a whole number

• A number that is always a decimal

Which of the following is a rational number?

• Square root of 2

• Pi

• 7

• e

Is -10 a rational number?

• Yes, because it can be expressed as a fraction

• No, because it is negative

• Yes, because it is a whole number

• No, because it is not a fraction

What makes a decimal number rational?

• It is a repeating or terminating decimal

• It is a decimal with no pattern

• It is a non-repeating decimal

• It is an infinite decimal

How can 2.277 be expressed as a rational number?

• As a whole number

• As a fraction 2277/1000

• As an irrational number

• As a repeating decimal

Is the square root of 1 a rational number?

• No, because it is not a whole number

• Yes, because it is an irrational number

• No, because it is a square root

• Yes, because it equals 1

Why is the square root of 8 considered irrational?

• Because it can be expressed as a fraction

• Because it is a repeating decimal

• Because it is a whole number

• Because it cannot be expressed as a fraction of whole numbers

What did the Greeks think about irrational numbers?

• They were confused and rejected them

• They embraced them as part of mathematics

• They ignored them completely

• They used them in music

How are fractions related to music according to the Greeks?

• Fractions have no relation to music

• Music intervals can be expressed as fractions

• Music is based on irrational numbers

• Fractions are only used in mathematics

What is an octave in music in terms of fractions?

• A fraction of 1 to 2

• A fraction of 3 to 4

• A fraction of 1 to 3

• A fraction of 2 to 3