Read, represent, compare, and order decimals to thousandths

Ontario Grade 6 Mathematics

Number

Ontario Grade 6 Mathematics — B1.4

A decimal names a number that may include a part less than one whole. You already know that digits have places, such as ones and tenths. This lesson adds hundredths and thousandths. A thousandth is one of one thousand equal parts of a whole. You will read, represent, compare, and order decimals with up to three places after the decimal point. All example numbers are made for practice; they are not measurements.

What you will learn

Read decimals to thousandths using place-value names.
Represent decimals with place value and on a number line.
Compare decimals by checking place values from left to right.
Order decimals from least to greatest or greatest to least.

1. Read decimals with place value

The decimal point separates the whole-number part from the part less than one. In

4.286

, the

4

is in the ones place. After the decimal point, the places are tenths, hundredths, and thousandths, in that order.

A place-value name tells what a digit stands for. In

4.286

, the

2

means two tenths, the

8

means eight hundredths, and the

6

means six thousandths. Read the number as four and two hundred eighty-six thousandths.

Zeros can hold places. In

3.047

, the

0

shows that there are no tenths. The

4

is in the hundredths place, and the

7

is in the thousandths place. Read this as three and forty-seven thousandths. Keep the zero when writing the number so the other digits stay in their correct places.

A zero at the end of a decimal does not change its value. For example,

0.5

,

0.50

, and

0.500

all name five tenths. But a zero between digits can change their places. The numbers

0.506

and

0.56

do not have the same value.

0.1=\frac{1}{10},\quad 0.01=\frac{1}{100},\quad 0.001=\frac{1}{1000}

The first three places after the decimal point are tenths, hundredths, and thousandths.
A zero can hold a place even when it adds no amount.
Zeros added or removed at the end of a decimal do not change its value.

2. Represent and compare decimals

You can represent a decimal by naming its places or locating it on a number line. A number line shows numbers in order. Numbers farther to the right are greater. For example,

0.6

is to the left of

0.7

, so

0.6

is less than

0.7

.

To compare two decimals, first compare their whole-number parts. If those are equal, compare the tenths digits. If those are equal too, compare the hundredths digits, then the thousandths digits. Stop at the first place where the digits differ. That place tells which number is greater.

Consider

2.407

and

2.39

. Their whole-number parts are both

2

. Write

2.39

as

2.390

to show three decimal places. At the tenths place, the digits are

4

and

3

. Since

4

is greater than

3

,

2.407

is greater. There is no need to compare later places once the first difference is found.

The symbol

<

means “is less than.” The symbol

>

means “is greater than.” The symbol

=

means “has the same value as.” For example,

0.62<0.70

says that sixty-two hundredths is less than seven tenths. Writing

0.7

as

0.70

can make the place values easier to see.

2.407>2.390

Compare from the whole-number part toward the smallest place.
The first place where digits differ decides the comparison.
Adding zeros at the end can help show matching places without changing value.

3. Order decimals and check

To order decimals, compare them and list them in the direction requested. Least to greatest starts with the smallest number. Greatest to least starts with the largest.

When decimals have different numbers of places, you can add zeros at the ends to show the same number of places. For example, write

1.5

,

1.08

, and

1.125

as

1.500

,

1.080

, and

1.125

. The whole-number parts match. The tenths digits show that

1.080

is smallest. Compare the remaining two: at the hundredths place,

1.125

has

2

and

1.500

has

0

. Therefore,

1.125

comes next, followed by

1.500

.

Check the direction in the question before giving your answer. For least to greatest, each number should be greater than or equal to the number before it. A number line can help you check: the values should move from left to right.

A decimal with fewer than three places still has a value at the thousandths place. For example,

0.8=0.800

. The added zeros show the places clearly; they do not change the number.

1.080<1.125<1.500

Use matching decimal places when that makes a comparison clearer.
For least to greatest, list values from smallest to largest.
Check that the order matches the words in the question.

Place-value chart for $2.583$

Ones	Tenths	Hundredths	Thousandths
2	5	8	3

Worked example

Read and represent a decimal

Read

5.032

in words. Identify the value shown by each digit after the decimal point.

Five and thirty-two thousandths

The point for $5.032$ is just to the right of $5$ on the line from $5$ to $6$.

Name the places
Starting just after the decimal point, the places are tenths, hundredths, and thousandths.
$5.032$
Read the decimal part
There are zero tenths, three hundredths, and two thousandths. The zero holds the tenths place, so the $3$ stays in the hundredths place.
$0.032=\frac{3}{100}+\frac{2}{1000}$
Say the number
Read the whole-number part, then the decimal part using thousandths. The number is five and thirty-two thousandths.

Answer:

5.032

is five and thirty-two thousandths. Its decimal digits show zero tenths, three hundredths, and two thousandths.

Check: The zero is needed. Without it, the

3

would be in the tenths place instead of the hundredths place.

Worked example

Compare two decimals

Which is greater,

0.608

or

0.68

? Use place value to explain.

Comparing decimals between six tenths and seven tenths

From left to right, the points are $0.6$, $0.608$, $0.68$, and $0.7$.

Show equal places
Write $0.68$ with three decimal places by adding a zero at the end. Its value stays the same.
$0.68=0.680$
Compare from left to right
The tenths digits both equal $6$ . At the hundredths place, $0$ is less than $8$ . So $0.608$ is less than $0.680$ .
$0.608<0.680$

Answer:

0.68

is greater than

0.608

.

Check: On a number line,

0.608

is to the left of

0.680

.

Worked example

Order three decimals

Order

3.5

,

3.057

, and

3.409

from least to greatest.

Three decimals in order

The points are shown from least to greatest, moving from left to right.

Show thousandths
Add zeros at the ends where needed. This gives each number three decimal places without changing its value.
$3.500,\quad 3.057,\quad 3.409$
Compare the numbers
The whole-number parts are all $3$ . The tenths digits are $5$ , $0$ , and $4$ . This makes $3.057$ the smallest and $3.500$ the greatest. The remaining number is $3.409$ .
$3.057<3.409<3.500$
Give the requested order
List the original decimals from least to greatest. The final number may be written as $3.5$ because it has the same value as $3.500$ .

Answer:

3.057

,

3.409

,

3.5

Check: The order goes from left to right on a number line. Also,

3.5=3.500

.

Common mistakes and how to avoid them

Thinking that a decimal with more digits must be greater.

Correction: Compare the place values from left to right. For example,

0.608

is less than

0.68

, even though it has more written digits.

Reading

4.06

as four and six tenths.

Correction: The

6

is in the hundredths place. Read

4.06

as four and six hundredths. The zero holds the tenths place.

Thinking that adding a zero at the end changes a decimal.

Correction: A zero at the end does not change the value. For example,

0.7=0.70=0.700

.

Giving an order in the wrong direction.

Correction: Check whether the question asks for least to greatest or greatest to least before listing the numbers.

Lesson summary

The first three places after the decimal point are tenths, hundredths, and thousandths.
Read each digit by its place. Keep zeros that hold places.
Compare from the whole-number part, then move through the decimal places from left to right.
Zeros added at the end can show matching places without changing value.
Order decimals in the direction the question asks.

Check your understanding

Question 1

Which is greater:

0.409

or

0.41

?

$0.409$
$0.41$
They are equal
$0.400$

Show answer and explanation

0.41

Write

0.41

as

0.410

. Since

0.409<0.410

,

0.41

is greater.

Question 2

Which list orders

2.08

,

2.8

, and

2.108

from least to greatest?

CAD 2.8, 2.108, 2.08
CAD 2.08, 2.108, 2.8
CAD 2.108, 2.08, 2.8
CAD 2.08, 2.8, 2.108

Show answer and explanation

CAD 2.08, 2.108, 2.8

Write the numbers as

2.080

,

2.800

, and

2.108

. Their order is

2.080<2.108<2.800

.

Key terms

Decimal point: The mark that separates the whole-number part from the part less than one.
Tenths: The first place to the right of the decimal point. One tenth is one of ten equal parts of a whole.
Hundredths: The second place to the right of the decimal point. One hundredth is one of one hundred equal parts of a whole.
Thousandths: The third place to the right of the decimal point. One thousandth is one of one thousand equal parts of a whole.
Number line: A line that shows numbers in order. Greater numbers are farther to the right.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation B1.4. 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.

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B1.4 · Read, represent, compare, and order decimals to thousandths

Ontario Grade 6 Mathematics

Ontario Grade 6 Mathematics — B1.4

What you will learn

1. Read decimals with place value

2. Represent and compare decimals

3. Order decimals and check

Place-value chart for $2.583$

Read and represent a decimal

Compare two decimals

Order three decimals

Common mistakes and how to avoid them

Lesson summary

Check your understanding

Question 1

Question 2

Key terms

Continue through Grade 6 Math

About this lesson and its review