Express probability as a fraction, decimal, or percent on a probability line

Ontario Grade 6 Mathematics

Data

Fractions, decimals, and percents on a probability line

A probability tells how likely something is to happen. A probability line helps us see how likely it is. We can write a probability as a fraction, a decimal, or a percent. In this lesson, you will connect these three forms and place them on a line from

0

to

1

.

What you will learn

Read a probability line from 0 to 1.
Show the same probability as a fraction, decimal, and percent.
Place a probability at the matching point on a probability line.

Start with the probability line

Imagine a bag with ten equal-sized counters: one is blue and nine are yellow. If one counter is chosen without looking, the chance of choosing blue is one out of ten. We can write this as

\frac{1}{10}

. This example is hypothetical.

A probability line shows how likely an event is. The left end,

0

, means impossible. The right end,

1

, means certain. A point between them shows a chance between impossible and certain. A chance near

0

is unlikely. A chance near

1

is likely.

A fraction names a part of a whole. In

\frac{1}{10}

, the whole is split into ten equal parts, and one part is chosen. A decimal is another way to write a number, such as

0.1

. A percent means a number of parts out of

100

, so 10% means ten out of one hundred.

These are three ways to express the same probability:

\frac{1}{10}=0.1=10\%

. On the probability line, all three forms belong at the same point.

0\leq P\leq 1

$0$ means impossible.
$1$ means certain.
A probability can be written as a fraction, decimal, or percent.

Connect fractions, decimals, and percents

To change a fraction to a decimal, think of the fraction as a division. For example,

\frac{1}{4}

means one divided by four, which is

0.25

. To change a decimal to a percent, read it as a number out of one hundred:

0.25

is 25%.

You can also use a familiar fraction. One half is

0.5

, or 50%. It sits halfway between

0

and

1

. A quarter is

0.25

, or 25%, so it sits one quarter of the way from

0

to

1

.

When placing a value, first notice its size. A probability of

0.25

is between

0

and

0.5

, and it is closer to

0

. A probability of

0.8

is between

0.5

and

1

, and it is closer to

1

.

A probability line can be marked with helpful reference points such as

0

,

0.5

, and

1

. The marks do not need to be equally spaced for every value, but the position must match the number. A larger probability belongs farther to the right.

0.25=25\%

A fraction can be read as a division to find its decimal form.
A decimal such as $0.25$ is 25%.
On the line, numbers increase from left to right.

Place and label a probability

Before plotting a probability, identify the values at the two ends of the line. Then locate a useful reference point, such as one half. Compare the probability with those values and place it between the correct marks.

Keep equivalent forms together. If a point is labelled

\frac{3}{4}

, it can also be labelled

0.75

and 75%. The point does not move when its name changes.

Check the result in two ways. First, make sure the value is between

0

and

1

. Second, make sure its position makes sense: a value closer to

1

should be farther right than a value closer to

0

.

\frac{3}{4}=0.75=75\%

Read the endpoints before placing a point.
Equivalent forms name the same location.
Check both the value and its position.

A quick practice routine

When you meet a probability, say its fraction, decimal, or percent form aloud. Then find the matching point on a line from

0

to

1

. If a form is unfamiliar, compare it with one half and with the endpoints.

For example,

0.6

is greater than

0.5

and less than

1

. So it belongs between the halfway point and the certain end. Its percent form is 60%.

Do not confuse the probability line with a line showing time or distance. Here, the whole interval represents all the way from impossible to certain. A probability is located by its value within that whole interval.

0.5<0.6<1

Convert or recognize an equivalent form before plotting.
Use $0.5$ as a useful halfway reference.
The probability line represents likelihood from impossible to certain.

Worked example

A quarter of the way

Write

\frac{1}{4}

as a decimal and a percent. Then locate it on a probability line.

One quarter on the probability line

The marked point is one quarter of the distance from impossible to certain.

Find the decimal
The fraction means one divided by four. One divided by four is $0.25$ .
$\frac{1}{4}=0.25$
Find the percent
The decimal $0.25$ is twenty-five hundredths, which is 25%.
$0.25=25\%$
Place the point
One quarter is less than one half, so place it between $0$ and $0.5$ , one quarter of the way from $0$ to $1$ .
$\frac{1}{4}=0.25=25\%$

Answer:

\frac{1}{4}=0.25=25\%

. Place the point at

0.25

.

Check: The point is between

0

and

0.5

, as a quarter should be.

Worked example

Seven tenths

A chance is given as

\frac{7}{10}

. Express it as a decimal and a percent, then locate it on a probability line.

Seven tenths on the probability line

The point at 0.7 is right of the halfway mark.

Write the decimal
Seven tenths is written as $0.7$ . The zero shows that there are no whole ones.
$\frac{7}{10}=0.7$
Write the percent
Seven tenths is the same amount as seventy hundredths, or 70%.
$0.7=70\%$
Locate the value
Since $0.7$ is greater than $0.5$ but less than $1$ , place it to the right of halfway and before certain.
$0.5<0.7<1$

Answer:

\frac{7}{10}=0.7=70\%

. Place the point at

0.7

.

Check: The point lies to the right of

0.5

and to the left of

1

.

Worked example

A spinner chance

A hypothetical spinner has eight equal sections. Three are green. Express the chance of landing on green as a fraction, decimal, and percent. Locate it on a probability line.

Three eighths on the probability line

The hypothetical spinner chance is marked at 0.375.

Write the fraction
There are eight equal sections in all, and three are green. The chance is three out of eight.
$\frac{3}{8}$
Convert to a decimal
Divide three by eight to get $0.375$ .
$3\div 8=0.375$
Convert to a percent
The decimal $0.375$ is thirty-seven and a half hundredths, so it is 37.5%.
$0.375=37.5\%$
Place the point
The value is less than $0.5$ , so it belongs left of halfway. It is a little less than $0.4$ .
$\frac{3}{8}=0.375=37.5\%$

Answer:

\frac{3}{8}=0.375=37.5\%

. Place the point at

0.375

.

Check: The point is between

0

and

0.5

, which fits a probability below one half.

Common mistakes and how to avoid them

Placing

0.7

to the left of

0.5

because seven is larger than five.

Correction: Compare the decimal values.

0.7

is greater than

0.5

, so it belongs to the right.

Treating

0.25

and 25% as different chances.

Correction: They are two forms of the same value, so they share one point on the probability line.

Placing a probability outside the line from

0

to

1

.

Correction: A probability on this line must be at least

0

and at most

1

.

Lesson summary

A probability line runs from $0$ , impossible, to $1$ , certain.
Fractions, decimals, and percents can name the same probability.
Place larger probabilities farther to the right.

Check your understanding

Question 1

Which forms are equal to

0.4

?

$\frac{4}{10}$ and 40%
$\frac{4}{100}$ and 4%
$\frac{1}{4}$ and 25%
correctIndex

Show answer and explanation

\frac{4}{10}

and 40%

\frac{4}{10}=0.4

, and

0.4=40\%

.

Question 2

Where should

0.8

be placed?

Between $0$ and $0.5$
At $0.5$
Between $0.5$ and $1$
correctIndex

Show answer and explanation

Between

0.5

and

1

0.8

is greater than

0.5

and less than

1

, so it belongs between them.

Question 3

A chance is

\frac{1}{5}

. What is its decimal form?

$0.2$
$0.5$
$0.8$
correctIndex

Show answer and explanation

0.2

One divided by five is

0.2

.

Key terms

Probability: A number that tells how likely something is to happen.
Probability line: A line from $0$ to $1$ that shows likelihood.
Percent: A way to describe a number of parts out of one hundred.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation D2.1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

Official curriculum reference

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D2.1 · Express probability as a fraction, decimal, or percent on a probability line

Ontario Grade 6 Mathematics

Fractions, decimals, and percents on a probability line

What you will learn

Start with the probability line

Connect fractions, decimals, and percents

Place and label a probability

A quick practice routine

A quarter of the way

Seven tenths

A spinner chance

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Question 3

Key terms

Continue through Grade 6 Math

About this lesson and its review