Read and represent whole numbers to one million

Ontario Grade 6 Mathematics

Number

Use place value to read, write, and show large whole numbers.

A large whole number can look hard to read at first. Place value makes it easier. Each digit has a place, and each place tells how much that digit is worth. In this lesson, you will work with whole numbers from zero to one million. You will read them, write them, and show how their digits make the number.

What you will learn

Explain the value of a digit by its place.
Read whole numbers up to one million in words.
Write a number shown in words or in expanded form.
Represent a whole number with a place-value chart or a labelled model.

1. Begin with place value

A whole number is a number with no part smaller than one. Examples include

8

,

240

, and

16{,}305

. The digits are the symbols

0

through

9

. A digit’s place tells its value in the number.

You already know ones, tens, and hundreds. In

472

, the

2

is in the ones place, the

7

is in the tens place, and the

4

is in the hundreds place. So the number has four hundreds, seven tens, and two ones.

For larger numbers, continue the places to the left. After hundreds come thousands, ten thousands, and hundred thousands. One million is the next named number after nine hundred ninety-nine thousand, nine hundred ninety-nine.

A place-value chart helps keep the places in order. Put one digit in each place. If a place has no groups, use a zero to hold that place. For example, the zero in

304{,}017

shows that there are no ten-thousands and no hundreds.

1{,}000{,}000

A digit’s place gives it a value.
Read a number in groups of three digits, starting from the right.
A zero can show that a place has no units of that kind.

2. Read and write numbers

A comma separates groups of three digits. Starting at the right, the first group is ones, the next is thousands, and the next is millions. For numbers up to one million, you will use at most the thousands group and the ones group, except for one million itself.

Read the thousands group first. Say “thousand” after it. Then read the ones group. For example,

63{,}408

is read as “sixty-three thousand, four hundred eight.” The comma marks the group break; it is not read aloud.

When writing a number named in words, decide how many thousands there are and how many ones remain. Write each group in its correct places. Keep zeros when a place within a group is empty. For example, “five thousand, twenty-six” has zero hundreds and zero tens in the ones group, so it is written

5{,}026

.

The number one million is written with a one in the millions place and zeros in all the smaller places. It is the upper limit in this lesson.

63{,}408=63{,}000+408

Read the thousands group before the ones group.
Use a comma to separate the groups of three digits.
Do not leave out placeholder zeros when a place is empty.

3. Show what the digits mean

You can represent a number in more than one way. A representation is a way to show a number. A place-value chart shows the position of each digit. Expanded form shows the value of each non-zero digit added together.

For example,

52{,}306

has five ten-thousands, two thousands, three hundreds, zero tens, and six ones. Its expanded form is

50{,}000+2{,}000+300+6

. The zero tens do not add anything, but the zero still helps show the correct place of the other digits.

You can also describe a number with groups. The number

52{,}306

is fifty-two thousand, three hundred six. These three ways—words, a place-value chart, and expanded form—show the same number.

Check a representation by making sure every digit is in the right place. In expanded form, add the parts to see whether they make the original number. In a chart, read the digits from left to right and check the comma group.

52{,}306=50{,}000+2{,}000+300+6

Expanded form separates a number into the values of its digits.
A zero may be important in the standard written number even when it adds no value in expanded form.
Different representations can show the same whole number.

4. A careful checking routine

When you read or write a large number, pause at the comma. Read the thousands group as a number, then say “thousand,” and then read the ones group. If the last group begins with a zero, do not say extra place names. Read only the number it makes.

When you start from words, mark the groups in your thinking: thousands, then ones. Fill every place in each group, including empty places with zeros. Then read your written number aloud to check it.

A number-place chart is useful when digits seem to move around. A digit moved one place to the left has a different value, so check the column headings before you finish.

Check the group names and the place of every digit.
Read the written answer aloud to check that it matches the words.
Use zeros to keep digits in their correct places.

Place-value chart for $52{,}306$

Ten-thousands	Thousands	Hundreds	Tens	Ones
5	2	3	0	6
$50{,}000$	$2{,}000$	$300$	$0$	$6$

Worked example

Read a number with zero places

Read

407{,}032

in words and describe the value of each non-zero digit.

Separate the groups
The comma separates the thousands group from the ones group. The groups are $407$ and $032$ .
$407{,}032$
Read each group
Read $407$ as four hundred seven, then say “thousand.” Read $032$ as thirty-two. The zero at the start of that group does not add a spoken place name.
Name digit values
The $4$ is worth four hundred thousand, the $7$ is worth seven thousand, the $3$ is worth thirty, and the $2$ is worth two. The zero digits show empty places.
$400{,}000+7{,}000+30+2$

Answer: Four hundred seven thousand, thirty-two.

Check: The expanded values add to

407{,}032

, and the zero places are kept in the written number.

Worked example

Write a number from words

Write “eighty-six thousand, five hundred nine” as a numeral and in expanded form.

Make the groups
“Eighty-six thousand” gives the thousands group, $86$ . “Five hundred nine” gives the ones group, $509$ .
$86\mid509$
Keep the places
Write the groups with a comma between them. The ones group has a zero in the tens place, so keep it.
$86{,}509$
Show the digit values
The digits represent eight ten-thousands, six thousands, five hundreds, no tens, and nine ones.
$80{,}000+6{,}000+500+9$

Answer:

86{,}509

; expanded form:

80{,}000+6{,}000+500+9

.

Check: Reading

86{,}509

aloud gives “eighty-six thousand, five hundred nine,” so the groups match.

Worked example

Use a place-value chart

A place-value chart shows 3 hundred-thousands, 0 ten-thousands, 8 thousands, 2 hundreds, 0 tens, and 4 ones. Write the number in standard form, words, and expanded form.

Put digits in order
Write the digits from hundred-thousands to ones, keeping each zero in its stated place.
$308{,}204$
Read the groups
The thousands group is $308$ , and the ones group is $204$ . Read each group in order.
Write expanded form
Add the values of the non-zero digits. The zero ten-thousands and zero tens contribute no amount.
$300{,}000+8{,}000+200+4$

Answer: Standard form:

308{,}204

. Words: three hundred eight thousand, two hundred four. Expanded form:

300{,}000+8{,}000+200+4

.

Check: The number has six places, and the digits match the chart from left to right.

Common mistakes and how to avoid them

Leaving out a zero when writing a number from words.

Correction: Fill every place in each group. “Five thousand, twenty-six” needs zeros for hundreds and tens:

5{,}026

.

Reading each digit separately instead of reading the groups as numbers.

Correction: Read each group of three digits as a number, then name the group. Read

63{,}408

as “sixty-three thousand, four hundred eight.”

Treating a digit as having the same value wherever it appears.

Correction: Check the place. In

4{,}040

, the two fours have different values: four thousand and forty.

Lesson summary

Place value tells what each digit is worth.
Commas separate groups of three digits, starting from the right.
Read the thousands group before the ones group.
Expanded form adds the values of the non-zero digits.
Keep zeros when they hold places in the written number.

Check your understanding

Question 1

How do you read

205{,}016

?

Two hundred five thousand, sixteen
Twenty-five thousand, sixteen
Two hundred five thousand, one hundred six
Two hundred fifty thousand, sixteen

Show answer and explanation

Two hundred five thousand, sixteen

The groups are

205

and

016

. Read them as two hundred five thousand and sixteen.

Question 2

Which numeral matches “forty-two thousand, seven hundred three”?

$42{,}073$
$42{,}703$
$4{,}273$
$427{,}003$

Show answer and explanation

42{,}703

The thousands group is

42

, and the ones group is

703

, so the numeral is

42{,}703

.

Question 3

Which expanded form represents

610{,}208

?

$600{,}000+10{,}000+200+8$
$600{,}000+1{,}000+200+8$
$60{,}000+10{,}000+200+8$
$600{,}000+10{,}000+20+8$

Show answer and explanation

600{,}000+10{,}000+200+8

The digits show six hundred thousand, one ten-thousand, two hundreds, and eight ones.

Key terms

Digit: One of the symbols from $0$ to $9$ used to write numbers.
Place value: The value a digit has because of its position in a number.
Expanded form: A way to write a number as the sum of the values of its digits.
Standard form: A number written with digits, such as $52{,}306$ .

Continue through Grade 6 Math

View the complete Grade 6 Math Ontario Grade 6 Mathematics curriculum and lessons

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation B1.1. 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

Report a correction or ask a question

B1.1 · Read and represent whole numbers to one million

Ontario Grade 6 Mathematics

Use place value to read, write, and show large whole numbers.

What you will learn

1. Begin with place value

2. Read and write numbers

3. Show what the digits mean

4. A careful checking routine

Place-value chart for $52{,}306$

Read a number with zero places

Write a number from words

Use a place-value chart

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