1-1 & 1-2: Rational & Irrational Numbers (11/19/24)

Front

What is a rational number?

Back

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \). Examples include \( \frac{1}{2}, 0.75, \) and \( -3 \).

Front

What is an irrational number?

Back

An irrational number is a number that cannot be expressed as a simple fraction. It has a non-repeating, non-terminating decimal expansion. Examples include \( \pi \) and \( \sqrt{2} \).

Front

What is a terminating decimal?

Back

A terminating decimal is a decimal that has a finite number of digits after the decimal point. For example, 2.75 and 0.5 are terminating decimals.

Front

What is a repeating decimal?

Back

A repeating decimal is a decimal that has one or more digits that repeat infinitely. For example, 0.666... (which is equal to \( \frac{2}{3} \)) is a repeating decimal.

Front

How do you convert a repeating decimal to a fraction?

Back

To convert a repeating decimal to a fraction, let \( x \) equal the decimal, multiply by a power of 10 to shift the decimal point, and then subtract the original equation from this new equation to solve for \( x \).

Front

What is the square root of 27?

Back

The square root of 27 is approximately 5.196, which lies between the whole numbers 5 and 6.

Front

Is the number \( \pi \) rational or irrational?

Back

The number \( \pi \) is an irrational number because it cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating.

Front

What is a mixed number?

Back

A mixed number is a whole number combined with a proper fraction. For example, \( 2 \frac{3}{4} \) is a mixed number.

Front

How do you convert a decimal to a fraction?

Back

To convert a decimal to a fraction, write the decimal as \( \frac{decimal}{1} \), then multiply the numerator and denominator by 10 raised to the number of decimal places.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal expansions.