0.2: Base-10 Number System
The Base-10 Number System
From Alphabitia to Base-10
Remember Alphabitia, where letters and blocks represented numbers? Each symbol’s position determined its value. Base-10 works the same way but uses digits 0–9.
Base-10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
Alphabitia Note: Just like in Alphabitia, “units,” “longs,” and “flats” show that position matters!
In this chapter, we will use the following symbols:
-
-
-
Unit:
* -
Long (10 units):
| -
Flat (100 units): 🟪
-
-
Place Value in Base-10
Each digit’s place tells us its value.
Example: Explore the number 482 in Base-10
| Place | Hundreds | Tens | Ones |
|---|---|---|---|
| Digit | 4 | 8 | 2 |
| Value | 400 | 80 | 2 |
Check: 482 = 400 + 80 + 2
Visual blocks version:
4 flats (🟪🟪🟪🟪) = 400
8 longs (||||||||) = 80
2 units (****) = 2
Grouping in Base-10
In base-10, every ten objects move up to the next place:
Example: Explore the base-10 number 47
You have 47 units (***********************************************)… feel free to count these if you want:
-
4 tens (🟦🟦🟦🟦)
-
7 units (🟩🟩🟩🟩🟩🟩🟩)
Result: 47 = 4 tens + 7 ones
Writing Numbers in Base-10
Numbers are written using digits 0–9, with each showing how many of each place.
Example: Exploring the number 356 in base-10
356
| Place | Hundreds | Tens | Ones |
|---|---|---|---|
| Digit | 3 | 5 | 6 |
| Value | 300 | 50 | 6 |
Blocks Version:
-
3 flats (🟪 🟪 🟪) = 300
-
5 longs (|||||) = 50
-
6 units (******) =6
Quick Practice
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Identify the place value of each digit in 2,407.
Solution: 2 is in the thousands place, 4 is in the hundreds place, 0 is in the tens place, and 7 is in the ones place.
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Write 4,215 as a sum of thousands, hundreds, tens, and ones, and draw the blocks.Solution:
1,000 + 1,000 + 1,000+ 1,000+ 100+100 + 10 + 1 + 1 + 1 + 1 +1
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If you have 73 units, how many tens and units do you have in base-10? Draw a block diagram. Solution: You will have 7 tens and 3 units.
