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Lesson Explainer: Place Value of Numbers up to 1 000 000 Mathematics • 4th Grade

In this explainer, we will learn how to write numbers up to one million in standard, word, and expanded forms and state the value of any digit.

We already know about place values up to 5 digits.

We can write numbers in lots of different ways, including

  • standard form,
  • word form,
  • expanded form.

An abacus can be useful when reading large numbers as each column represents a place value.

This abacus shows one number.

We can write this number in standard form by simply writing the number of beads in each place value (remember to write a 0 when its empty!): 231201

This number is written in standard form.

Definition: Standard Form

Standard form is the way we normally write numbers, using numerical digits: 231201

Example 1: Writing Numbers in Standard Form

Write down the number given in the figure in digits.

Answer

Writing a number in digits is known as standard form.

We can use a place value chart to help us write large numbers from models in standard form.

We complete the place value chart by writing the number of beads in each place value.

So, the number shown on the abacus is 166‎ ‎235.

Writing numbers in different ways allows us to understand what the digits mean.

By looking at the numbers of beads and where they are in relation to the place values, we can write the place value of each digit.

There are 2 beads in the hundred thousands column.

This can be described as 2 hundred thousands.

We can express the whole number in this way by writing
2 hundred thousands
3 ten thousands
1 thousand
2 hundreds
0 tens
1 one

Example 2: Identifying Place Values

What is the value of the digit 4 in the number 459‎ ‎862?

Answer

Putting our number in a place value chart can help us to identify which place value the digit 4 is in.

From the place value chart, we can see that the digit 4 is in the hundred thousands column.

This means that the value of the digit 4 in the number is 4 hundred thousand.

Another way of breaking up numbers is to use the expanded form.

In expanded form, our number 231‎ ‎201 would be 200000+30000+1000+200+0+1.

We have separated the number into place values but shown the actual value of each digit. This can be useful when using the numbers in calculations such as addition or subtraction.

Definition: Expanded Form

Expanded form is when numbers have been broken down and shown as the value of each digit: 200000+30000+1000+200+0+1.

Example 3: Identifying Digits in Expanded Form

What value does the digit 9 represent in the number 569‎ ‎824?

Answer

Showing the value of a digit in a number is one way of using the expanded form.

We can use a place value chart to help us find the value of the digit 9 in our number.

The digit 9 is in our one thousands column. This means that there are 9 one thousands.

To find the value of this number, we can write this as a number sentence: 99×1000,9×1000=9000.onethousandsisthesameas

So, the value of the digit 9 in the number is 9‎ ‎000.

Numbers can also be written in words.

When we write or talk about numbers in words, we group the place values.

On our abacus, we can see that the words hundreds, tens, and ones all appear twice.

Let’s look at a place value grid.

Again hundreds, tens, and ones appear twice. The difference is the value of the numbers.

On the left, we have

  • hundred thousands (100‎ ‎000),
  • ten thousands (10‎ ‎000),
  • one thousands (1‎ ‎000).

On the right, we have

  • hundreds (100),
  • tens (10),
  • ones (1).

We call each of these groups of three digits a period.

In the number above, we have two periods: the thousands period and the ones period.

Each period is separated by a comma:

Definition: Period

A period is each group of three digits in large numbers.

Definition: Word Form

Word form is when numbers have been written entirely in words: twohundredthirty-onethousand,twohundredone.

Example 4: Writing Numbers in Word Form

Express 465‎ ‎232 in words.

Answer

To help us write this number in words, we can look at the number of periods in the number.

This means for 465‎ ‎232 there are two periods: the thousands period and the ones period.

The thousands period is written as fourhundredsixty-vethousands.

The ones period is written as twohundredthirty-two.

When written together, the two periods should be separated by a comma: fourhundredsixty-vethousand,twohundredthirty-two.

The highest number we can write using 2 periods is 999‎ ‎999.

Any number higher than this will need a new place value column. Since periods are in groups of 3, this will also be the start of a new period.

The next number would be 1000000

This number will split into 3 periods.

This new number is called 1 million.

Let’s recap what we have learned in this explainer.

Key Points

  • Numbers can be written in standard, word, and expanded forms.
    StandardWordExpanded
    231‎ ‎201Two hundred thirty-one thousand, two hundred one200‎ ‎000+
    30‎ ‎000+
    1‎ ‎000+
    200 +
    0 +
    1
  • Large numbers are separated into periods to make them easier to read.
  • The value of a digit is based on its place value position.

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