Rational Numbers on the Number Line – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Representing rational numbers by placing them on a number line or reading given points on a number line can be tough at first glance. But once you understand how units on number lines help you, you will master it in no time.

Rational numbers can be integers, fractions, or decimals. And remember, they can be positive numbers as well as negative numbers. That is why a number line is a line that extends in both directions up to infinity. There is one convention: positive numbers are always on the right side of zero.

Number lines can have different scales according to what they represent. There can be number lines with units of integers such as -3, -2, -1, 0, 1, 2, 3, and so on. Keep in mind, you don’t always have to display 0 on the number line, especially if you have to include large numbers that are all in close proximity of one another on the number line.

When representing terminating decimals, you might need to use a different scale, with units of 0.1 or even 0.01 such as -0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3 or -0.03, -0.02, -0.01, 0, 0.01, 0.02, 0.03, and so on.

To represent fractions, you need to look for the least common denominator of all the fractions you want to place on the number line and then divide the space between the integers on the number line in the exact amount of units. If you have all fractions over 6, for example, divide your number line in -1, -5/6, -4/6, -3/6, -2/6, -1/6, 0, 1/6 , 2/6, and so on.

When reading numbers on a number line, look at the units. If you have 10 units between integers, and aren't given more specific instructions, you can either write the number in decimal form or in fraction form (over 10). If you have more or less than 10 units, they probably represent fractions. Just count the units between the integers, for example 7, and you know that the first unit after zero represents 1/7, the second 2/7, and so on.

Repeating decimals cannot been shown on the number line accurately, it is therefore best to write them as a fraction.

Apply and extend previous understandings of operations with fractions.

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Exercises in this Practice Problem
Explain how far Tim is above the water shortly after jumping.
Determine the decimals and fractions which equal the given values.
Find the height of each jump in feet and inches.
Convert the depths to see which diver dove deepest.
Identify the steps for converting height from fraction to decimal form.
Find out which distances Marshall ran this week.