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Learning Goals

We are learning to read decimal numbers up to thousandths.

​

We are learning to represent decimal numbers in different forms.

B1.4 read, represent, compare, and order decimal numbers up to thousandths, in various contexts.             

Grade 6 Ontario Math Curriculum, 2022.

Success Criteria

By the end of this lesson, I can:

Read decimals correctly

​

Use the word “and” to show the decimal point when reading or writing decimals in word form

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Represent decimals in various ways (e.g., standard form, expanded notation)

Let’s Explore Decimals – Now with Thousandths!

We have already learned about decimals with tenths and hundredths. Now, we will explore decimals up to the thousandths place. 

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Decimal numbers that include thousandths have three digits after the decimal point. Here is an example: 1.764

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• Decimals can be less than one:�Example: 0.532�This means 532 thousandths, or a part of a whole that is less than one.��
• Decimals can also be greater than one:�Example: 16.139�This means 16 whole units and 139 thousandths—a whole number combined with a decimal part.

What Is the Value of One Thousandth?

Here is one whole.

Let’s see what happens if we divide one whole into 10 equal parts.

What Is the Value of One Thousandth?

One whole has been divided into 10 equal parts.

Each part represents one tenth.

0.1

What Is the Value of One Thousandth?

Let’s see what happens if we divide one whole into 100 equal parts.

What Is the Value of One Thousandth?

One whole has been divided into 100 equal parts.

Each part represents one hundredth.

0.01

What Is the Value of One Thousandth?

Let’s see what happens if we divide one whole into 1000 equal parts.

What Is the Value of One Thousandth?

One whole has been divided into 1000 equal parts.

Each part represents one thousandth.

0.001

Representing Decimals

There are many different ways we can represent decimals. We will explore seven forms, which are in:

• Place value chart
• Word form
• Standard form
• Expanded form
• Expanded notation
• Expanded notation using fractions

Place Value

Let’s begin by looking at representing decimals on a place value chart.

The place value of the three positions to the right of the decimal point are tenths, hundredths, and thousandths.

Let’s use the number 12.764 as an example and place it on a value place chart.

1

2

7

6

4

Let’s Practice

For the following decimals, place each numeral in the correct place value: 

3.653

​

25.276

Let’s check our answers!

tens

2

3

5

6

2

5

7

3

6

Word Form

Another way to represent decimals is in word form.

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Let’s take the number 2.853 as an example.

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We read this as, “two and eight hundred fifty-three thousandths.”

• The word “and” represents the decimal point.
• We say “and” after naming the whole number part ("two and...").
• The place value of the last digit tells us how to end the number. In this case, the 3 is in the thousandths place, so we say “thousandths.”

Let’s Practice

Read each decimal below and write it in standard form.

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Four and seven hundred thirty-two thousandths

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Sixteen and three hundred twenty-three thousandths

Let’s check our answers!

4.732

16.323

Standard Form

We can represent decimals in standard form. 

​

Standard form is when we use numerals with a decimal point.

Here are some examples:

0.206

2.853

11.822

�

Let’s Practice

Read each decimal below and write it in word form.

6.553

9.806

Let’s check our answers!

six and five hundred fifty-three thousandths

nine and eight hundred six thousandths

Expanded Form

We can also represent decimals in expanded form. 

Beginning from the left of the decimal, we will identify each digit’s place value.

The 7 is in the ones place, so its value is

The 3 is in the tenths place, so its value is

The 6 is in the hundredths place, so its value is

The 1 is in the thousandths place, so its value is

Then, show each value as separate terms, placed together as such:

7.361 = 7 + 0.3 + 0.06 + 0.001

7

0.3

0.06

0.001

Expanded form is when we decompose (break down) a number based on the place value of each digit.

Let’s represent 7.361 in expanded form.

Let’s Practice

Now it’s your turn to practice!

Write the following decimals in expanded form:

8.672

19.327

�

Let’s check our answers!

8.672 = 8 + 0.6 + 0.07 + 0.002

19.327 = 10 + 9 + 0.3 + 0.002 + 0.007

Expanded Form

Similar to expanded form, expanded notation decomposes numbers according to their place value. The difference is that in addition to place value, multiplication is used to show the value of each digit.

Beginning from the left of the decimal, we will identify each digit’s place value.

The 7 is in the ones place, so its value is 7 x 1

The 3 is in the tenths place, so its value is 3 x 0.1

The 6 is in the hundredths place, so its value is 6 x 0.01

The 1 is in the thousandths place, so its value is 1 x 0.001

Then, show each value as separate terms, placed together as such:

(7 x 1) + (3 x 0.1) + (6 x 0.01) + (1 x 0.001)

�

Each digit is multiplied by its place value.

Let’s use the same example previously used: 7.361

Let’s Practice

Write the following decimals in expanded notation:

7.452

24.115�

Let’s check our answers!

(7 x 1) + (4 x 0.1) + (5 x 0.01) + (2 x 0.001)

(2 x 10) + (4 x 1) + (1 x 0.1) + (1 x 0.01) + (5 x 0.001)

Expanded Form

Lastly, we can also represent decimals using fractions!

Let’s continue with the decimal 7.361

The 7 is in the ones place, so its value is 7 x 1

The 3 is in the tenths place, so its value is 3 x

The 6 is in the hundredths place, so its value is 6 x

The 1 is in the thousandths place, so its value is 1 x

Then, show each value as separate terms, placed together as such:

(7 x 1) + (3 x ) + (6 x ) + (1 x )

Each digit is multiplied by its place value which is shown as a fraction.

Tenths =   Hundredths =   Thousandths =

Beginning from the left of the decimal, we will identify each digit’s place value.�

Let’s Practice

Write the following decimals in expanded notation using fractions:

5.826

13.628

Let’s check our answers!

(5 x 1) + (8 x 1/10) + (2 x 1/100) + (6 x 1/1000)

(1 x 10) + (3 x 1) + (6 x 1/10) + (2 x 1/100) + (8 x 1/1000)

Let’s Review

Today, we learned how to:

Let’s Continue to Practice!

We’ll continue practicing how to read and represent decimal numbers with various activities, including:

• Representing Decimals in Expanded Notation Activity Sheet here
• Decimals in Standard and Word Form Activity Sheet here
• Reading and Representing Decimals up to Thousandths Activity Sheet here