Base 10 Numerals - Definition, Examples, Facts & Quiz, FAQ, Trivia
Learn about place values, the base ten number system, and expanded form with visual examples
What Are Base Ten Numerals?
Base ten numerals are the numbers we use every day - 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. We call this the base ten number system because it's based on groups of ten.
Here's how it works:
• Ones place: When we count to 9, we use single digits.
• Tens place: After 9 comes 10 - that's one group of ten and zero ones.
• Hundreds place: Ten groups of ten make one hundred (100).
This pattern continues with thousands, ten-thousands, and so on. Each place is ten times bigger than the place to its right.
Key Concept
Our number system has only ten digits (0-9), but we can write any number by combining them and using place values.
Understanding Place Values
Place value tells us what each digit in a number represents based on its position. Let's look at the number 3,482:
This means:
• 3 thousands = 3 × 1,000 = 3,000
• 4 hundreds = 4 × 100 = 400
• 8 tens = 8 × 10 = 80
• 2 ones = 2 × 1 = 2
When we add them together: 3,000 + 400 + 80 + 2 = 3,482
Remember
Each place is ten times bigger than the place to its right. Moving left increases the value by a factor of 10.
Expanded Form
Expanded form shows a number broken down into the sum of each digit multiplied by its place value. This helps us understand what each digit represents.
Example 1: 728
Practice Tip
Try writing numbers in expanded form by first identifying each digit's place value, then writing out the multiplication.
Practice Quiz
Test your understanding of base ten numerals with these practice questions
Frequently Asked Questions
Here are answers to common questions about base ten numerals:
Number Trivia
Discover interesting facts about numbers and counting systems:
Ancient Counting
The earliest known number system was used by the Sumerians around 3000 BC. They used a base 60 system (sexagesimal) which is why we have 60 seconds in a minute and 60 minutes in an hour.
Binary System
Computers use base 2 (binary) because it's easier to represent with electrical circuits (on/off). In binary, 10 actually represents the number 2 in our base ten system!
Largest Number
The largest named number is the googolplex, which is 10 raised to the power of a googol (a googol is 1 followed by 100 zeros). There isn't enough space in the universe to write out all the zeros in a googolplex!
Different Counting
Some languages have different counting systems. In French, 80 is "quatre-vingts" (four twenties), and 99 is "quatre-vingt-dix-neuf" (four twenties plus nineteen).
