Rational Numbers Overview

Click on the flashcard to see the answer



What are rational numbers?

Rational numbers are numbers that can be expressed as the fraction of two integers, with the denominator not equal to zero.

Give an example of a rational number.

Examples include 1/2, -3/4, and 5, where 5 can be written as 5/1.

Are all integers rational numbers?

Yes, because any integer n can be expressed as n/1.

Is the number 0 a rational number?

Yes, because it can be expressed as 0/1.

Can rational numbers be negative?

Yes, rational numbers can be negative if either the numerator or the denominator is negative, but not both.

Is 0.75 a rational number? Why?

Yes, because it can be expressed as the fraction 3/4.

What makes a number not rational?

A number is not rational if it cannot be expressed as a fraction of two integers, like the square root of 2 or pi.

How do you convert a repeating decimal into a rational number?

Use algebra to set the decimal equal to a variable, shift the decimal point, subtract, and solve for the variable.

What is the relationship between rational numbers and decimals?

Rational numbers can be expressed as either terminating or repeating decimals.

Is -7/9 a rational number?

Yes, because it is a fraction of two integers with non-zero denominator.

Can a whole number be a rational number?

Yes, any whole number is a rational number because it can be written as that number over 1.

Is the fraction 16/8 a rational number? Why?

Yes, because it is the fraction of two integers and equals 2, an integer itself.

What is a common property of all rational numbers?

They can all be expressed as fractions or ratios of two numbers.

Do rational numbers form a subset of real numbers?

Yes, rational numbers are a subset of real numbers.

How are rational numbers used in everyday life?

They are used in measuring, dividing things into parts, and any situation involving ratios or fractions.





Test Your Knowledge

Select the correct option


1. What are rational numbers?

Numbers that can be expressed as integers only.

Numbers that can be expressed as the fraction of two integers, with the denominator not equal to zero.

Numbers that cannot be expressed as a fraction.

Numbers that are not whole numbers.

2. Give an example of a rational number.

0.3333

Square root of 2

Pi

-3/4

3. Are all integers rational numbers?

No, only even integers are rational.

Only integers that are perfect squares.

Yes, because any integer n can be expressed as n/1.

No, integers are not fractions.

4. Is the number 0 a rational number?

No, zero cannot be expressed as a fraction.

No, it is neither positive nor negative.

Yes, because it can be expressed as 0/1.

No, zero is not a number at all.

5. Can rational numbers be negative?

No, rational numbers must be positive.

Yes, rational numbers can be negative if either the numerator or the denominator is negative, but not both.

Only if both numerator and denominator are negative.

No, they can only be positive.

6. Is 0.75 a rational number? Why?

Yes, because it can be expressed as the fraction 3/4.

No, because decimals cannot be rational.

Yes, because all decimals are rational.

No, it cannot be expressed as a fraction.

7. What makes a number not rational?

The number can be expressed as a ratio of two integers.

A number is not rational if it cannot be expressed as a fraction of two integers, like the square root of 2 or pi.

The number is less than zero.

The number is positive.

8. How do you convert a repeating decimal into a rational number?

Count the repeating part and multiply by ten.

Use long division.

Use algebra to set the decimal equal to a variable, shift the decimal point, subtract, and solve for the variable.

Simply round the number to the nearest whole number.

9. What is the relationship between rational numbers and decimals?

Rational numbers can be expressed as non-repeating, non-terminating decimals.

Rational numbers can be expressed as either terminating or repeating decimals.

Rational numbers are always finite decimals.

Rational numbers can never be decimals.

10. Is -7/9 a rational number?

Yes, because it is a fraction of two integers with non-zero denominator.

No, because it is a negative fraction.

No, fractions cannot be negative.

Yes, but only if it is a positive fraction.

11. Can a whole number be a rational number?

Only negative whole numbers can be rational.

Yes, any whole number is a rational number because it can be written as that number over 1.

No, whole numbers are never rational.

Whole numbers are always irrational.

12. Is the fraction 16/8 a rational number? Why?

No, because it simplifies to 2 which is not a fraction.

Yes, because it is the fraction of two integers and equals 2, an integer itself.

No, because the numerator is larger than the denominator.

Yes, because any fraction cannot be simplified.

13. What is a common property of all rational numbers?

They always result in non-terminating decimals.

They can all be expressed as fractions or ratios of two numbers.

They are all greater than zero.

They are only whole numbers.

14. Do rational numbers form a subset of real numbers?

Yes, rational numbers are a subset of real numbers.

No, rational numbers and real numbers are the same.

No, rational numbers form a subset of integers.

Yes, but only when positive.

15. How are rational numbers used in everyday life?

They are only used in advanced mathematics.

They are used only in geometry.

They are used in measuring, dividing things into parts, and any situation involving ratios or fractions.

They are rarely used outside finance.