Base 10 and Place Value (gentle intro)
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn how our number system uses base 10 and what place value means for ones, tens, and hundreds.
The Concept
Section titled “The Concept”Base 10 means we group numbers by 10s. 10 ones make 1 ten, 10 tens make 1 hundred, and so on. Why 10? Most likely because we have 10 fingers:
Humans have counted on their fingers for thousands of years, so it’s natural that our number system groups by 10s.
But base 10 isn’t the only option. A “base” is just how many digits a system uses before it rolls over to the next place:
- Base 2 (binary) - uses only 0 and 1. This is how computers think, since electronic switches are either off (0) or on (1).
- Base 16 (hexadecimal) - uses 0–9 plus A–F (16 symbols). Programmers use it as a shorthand for binary, and it shows up in color codes like #FF5733.
- Base 12 (duodecimal) - we still see traces of it: 12 hours on a clock, 12 inches in a foot, 12 eggs in a dozen.
- Base 60 (sexagesimal) - the ancient Babylonians used this, and it’s why we have 60 seconds in a minute and 60 minutes in an hour.
For everyday math, we use base 10, and that’s what the rest of this lesson focuses on.
On a number line, you can see how each group of 10 is one jump forward:
Place value tells what each digit is worth based on its position:
- Rightmost digit: ones place (×1)
- Next left: tens place (×10)
- Next left: hundreds place (×100)
Example: 347
- 7 is in the ones place → 7 × 1 = 7
- 4 is in the tens place → 4 × 10 = 40
- 3 is in the hundreds place → 3 × 100 = 300
Total: 300 + 40 + 7 = 347
Here’s where 347 sits on a number line, right between 300 and 400:
You can think of it as: hundreds | tens | ones 3 | 4 | 7
Worked Example
Section titled “Worked Example”Break down 562:
- 5 hundreds = 500
- 6 tens = 60
- 2 ones = 2 Total: 500 + 60 + 2 = 562
Write 408 as hundreds, tens, ones:
- 4 hundreds = 400
- 0 tens = 0
- 8 ones = 8 Total: 400 + 0 + 8 = 408
Real-World Application
Section titled “Real-World Application”Place value helps read prices, addresses, phone numbers, or scores:
- 125 dollars = 1 hundred + 2 tens + 5 ones
- House number 247 = 2 hundreds + 4 tens + 7 ones
- Score of 89 points = 8 tens + 9 ones
Understanding places makes big numbers less scary. Break them into groups of 10s and 100s.