Locate 7/2 on a number line. Which of the following steps is correct?

Move 3 units to the right and divide the next unit into 2 equal parts. Stop at the 1st part.

Move 3 units to the right and divide the next unit into 3 equal parts. Stop at the 1st part.

Move 3 units to the right and divide the next unit into 3 equal parts. Stop at the 2nd part.

Move 3 units to the right and divide the next unit into 2 equal parts. Stop at the 1st part.

Move 3 units to the right and divide the next unit into 2 equal parts. Stop at the 2nd part.

Locate -1.6 on a number line. Which of the following steps is correct?

Move 1 unit to the left, then divide the distance between -1 and -2 into 10 equal parts, and stop at the 6th part.

Move 1 unit to the left, then divide the distance between -1 and -2 into 10 equal parts, and stop at the 4th part.

Move 2 units to the left, then divide the distance between -2 and -3 into 10 equal parts, and stop at the 4th part.

Move 2 units to the left, then divide the distance between -2 and -1 into 10 equal parts, and stop at the 6th part.

Move 1 unit to the left, then divide the distance between -1 and -2 into 10 equal parts, and stop at the 6th part.

On a number line, where would −11/4 be located?

Move 2 units to the left and divide the next unit into 4 parts. Stop at the 3rd part.

Move 3 units to the left and divide the next unit into 4 parts. Stop at the 3rd part.

Move 2 units to the left and stop halfway to the next unit.

Move 2 units to the left and divide the next unit into 4 parts. Stop at the 3rd part.

Move 3 units to the left and stop halfway to the next unit.

Rational Numbers and Their Location on a Number Line

Q: What is the difference between a rational and an irrational number?

A rational number can be written as a fraction of two integers, such as two-thirds or 5. An irrational number cannot, because its decimal never ends and never repeats. Pi and the square root of 2 are irrational, while every fraction, integer and terminating or recurring decimal is rational.

Q: Is pi a rational number?

No, pi is irrational, not rational. Its decimal goes on forever with no repeating pattern. This means you cannot write pi as a fraction of two integers. That is the opposite of a rational number, which can always be written as such a fraction.

Q: Is 0 a rational number?

Yes, 0 is a rational number. Every integer is rational because you can write it as a fraction over 1. In the case of 0, you write it as 0/1. Both 0 and 1 are integers and the denominator is not zero, so 0 qualifies as rational.

Key concept

Rational numbers can be written as a fraction of two integers. This covers all fractions, integers and decimals that end or repeat. Irrational numbers cannot: their decimals never end or repeat, like π.

Rational Numbers and Their Location on a Number Line - introduction visual

Video Lesson

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$Rational Numbers and Their Location on a Number Line poster$

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Flashcards

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$Rational numbers explained with examples showing that fractions, integers, terminating decimals, and recurring decimals are rational numbers.$ Explaining that irrational numbers are non-terminating decimals without repeating patterns, with examples like π and √2.

Explaining that irrational numbers are non-terminating decimals without repeating patterns, with examples like π and √2.

$Locating the rational number and fraction 11/3 on a number line by dividing it into 3 and 2/3, demonstrating on number line.$

Locating the rational number and decimal -2.7 on a number line, shown as -2 minus 0.7.

What are Rational Numbers?

Rational numbers can be written as a fraction of two integers.
They include fractions, terminating decimals, integers, and recurring decimals.

Practice Questions

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Q1Easy

Which of the following numbers is a rational number?

Choose your answer to continue

Interactive Activity

Explore how rational numbers (decimals and fractions) are located on the line.

Drag the purple dot along the line

Rational Number Forms

Decimal

1.25

Fraction

Mixed

1.25 is 1 unit to the right of zero, and an additional 0.25.This is 25 out of 100 equal steps between 1 and 2.

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Students Also Ask

The questions students bump into most on this topic

What is the difference between a rational and an irrational number?

A rational number can be written as a fraction of two integers, such as two-thirds or 5. An irrational number cannot, because its decimal never ends and never repeats. Pi and the square root of 2 are irrational, while every fraction, integer and terminating or recurring decimal is rational.

Is pi a rational number?

No, pi is irrational, not rational. Its decimal goes on forever with no repeating pattern. This means you cannot write pi as a fraction of two integers. That is the opposite of a rational number, which can always be written as such a fraction.

Is 0 a rational number?

Yes, 0 is a rational number. Every integer is rational because you can write it as a fraction over 1. In the case of 0, you write it as 0/1. Both 0 and 1 are integers and the denominator is not zero, so 0 qualifies as rational.

Are all fractions rational numbers?

Yes, all fractions are rational numbers. A rational number is any value you can write as a fraction of two integers. A fraction already fits that definition. For example, two-thirds and negative six-fifths are both rational. Their numerators and denominators are integers, and the denominator is not zero.

Are recurring decimals rational numbers?

Yes, recurring decimals are rational numbers. A recurring decimal has digits that repeat in a pattern forever. Any such decimal can be written as a fraction. For example, 0.3 recurring equals one-third. This is why recurring decimals count as rational, even though their decimals do not stop.

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