Large Numbers Lesson: Reading and Writing Big Numbers

As we learn more about numbers, we discover they can grow very large-into the thousands, millions, and even billions. Learning how to read, write, and understand large numbers helps us build strong math skills. In this lesson, you will explore place value in large numbers, learn how to write numbers in words and digits, and understand how to break down and compare numbers with many digits.

Let's take a step-by-step approach to understanding how big numbers are built-and how we can work with them confidently.

Understanding Place Value in Large Numbers

Every digit in a number has a place value. The place value tells us how much the digit is worth based on its position.

Here is the place value chart up to millions:

So, in the number 5,478,123:

• The digit 5 is in the millions place and represents 5,000,000.
  
• The digit 7 is in the ten thousands place and represents 70,000.
  

Understanding place value helps you figure out the value of each digit in a number.

Reading and Writing Large Numbers

To read and write large numbers correctly, we break them into periods of three digits:

• Ones period (units, tens, hundreds)
  
• Thousands period (thousands, ten thousands, hundred thousands)
  
• Millions period (millions, ten millions, hundred millions)
  

We separate each period with a comma.

Example:
Number: 4,205,318
Read as: Four million, two hundred five thousand, three hundred eighteen

To write large numbers in digits from words, listen carefully to the groups of three.

Example:

"Three million, sixty thousand, twelve"
Written as: 3,060,012

Smallest and Largest Numbers by Digit Count

The smallest 6-digit number is 100,000
It has a 1 in the hundred-thousands place and zeros in all the other places.

The largest 6-digit number is 999,999

The smallest 7-digit number is 1,000,000
This is also called one million.

To find the largest number with no repeated digits, you arrange the largest digits first, without repeats.

Example:
The largest 7-digit number using all different digits is 9,876,543

Writing Numbers as Sums of Their Parts

You can break down large numbers by writing them as the sum of their place values. This helps you understand how numbers are built.

Example: Break down 351,102:

• 351,000 + 102 = 351,102
  You can also write it as:
  
• 300,000 + 50,000 + 1,000 + 100 + 2
  

This is called expanded form.

Expanded form shows the value of each digit clearly.

Place Value of a Specific Digit

The value of a digit depends on its position in the number.

Example:
Number: 567,123

• The digit 1 is in the hundreds place → Value = 100
  

Another example:
Number: 231,789

• The digit 1 is in the thousands place → Value = 1,000
  

Knowing how to identify the value of a digit helps you work with bigger numbers confidently.

Place Value of Zero

Zero doesn't have a value of its own-but it plays an important role in holding a place.

Example:
In the number 123,456,0, the zero is in the unit's place.

• Its value is 0, but it shows that there are no ones in the number.
  

If we removed that zero, the number would shift-which changes the actual value.

Take This Quiz:

Large Numbers Quiz

Identifying the Value of Words in Numbers

Sometimes numbers are written in words, and you need to turn them into digits.

Example:
"Five million, two hundred thousand, and one"
Write it as: 5,200,001

Another example:
"Four million, seventy thousand, thirty-two"
Write it as: 4,070,032

You can use the place value chart to make sure each word fits the correct spot in the number.

Comparing Large Numbers

To compare large numbers, start with the digit in the largest place (leftmost digit). Keep moving right until the digits are different.

Example:
Compare 3,456,789 and 3,457,000

• The first digits (3) are the same
  
• The next digits (4) are the same
  
• The next digits: 5 and 5 → same
  
• Then: 6 vs. 7 → 7 is larger, so 3,457,000 is greater
  

When two numbers are very close, look at every digit from left to right.

Place Value Practice Examples

Let's try identifying place values in a few more examples.

Example 1:
Number: 4,320,678

• The digit 2 is in the ten thousands place
  
• Its value is: 20,000
  

Example 2:
Number: 7,005,142

• The digit 5 is in the thousands place
  
• Its value is: 5,000
  

Being able to locate digits and explain their values helps you understand how large numbers are built.

Breaking Down Numbers with Missing Parts

Sometimes numbers are written as sums, and you need to find the missing part.

Example:

987,654,321 = 987,000,000 + _____ + 321

We know:

• 987,000,000 is the millions
  
• 321 is the ones
  
• What's missing is the thousands: 654,000
  

Answer: 654,000

This shows how each group of digits fits into a place value period-ones, thousands, and millions.