The rule of 10 in math is a divisibility rule that helps quickly determine if a number can be divided evenly by 10 without leaving a remainder.
Understanding the Divisibility Rule of 10
Here's the key idea:
- A number is divisible by 10 if and only if its last digit (the digit in the ones place) is a 0.
This rule is straightforward and makes dividing by 10 simple. No complicated calculations are needed. You just need to look at the last digit. The reference video "Divisibility Rule for 10 | Math with Mr. J - YouTube" confirms this by stating, "So does that number end in a zero? Yes. So it means that that number is divisible by 10."
Examples of the Rule of 10
Let's look at some numbers to illustrate how this works:
| Number | Last Digit | Divisible by 10? |
|---|---|---|
| 10 | 0 | Yes |
| 50 | 0 | Yes |
| 100 | 0 | Yes |
| 120 | 0 | Yes |
| 123 | 3 | No |
| 456 | 6 | No |
| 7890 | 0 | Yes |
| 10000 | 0 | Yes |
| 234567 | 7 | No |
Why Does This Rule Work?
The divisibility rule for 10 works because our number system is base-10. Every place value (ones, tens, hundreds, thousands, etc.) is a power of 10.
- A number like 230 is actually (2 x 100) + (3 x 10) + (0 x 1). The digits 2 and 3 represent multiples of powers of 10 and, therefore, are always divisible by 10.
- The final digit, 0 in this case, represents a multiple of 1.
- If the final digit is zero, then this also becomes a multiple of 10.
- Only if the ones digit is 0 does the entire number become a multiple of 10.
Practical Uses of the Rule of 10
- Simplifying Division: Quickly determine if a number can be evenly divided by 10.
- Estimating: Use it to approximate values.
- Checking Calculations: Double-check to see if calculations are reasonable.
- Everyday Math: In situations requiring division or multiplication by 10.
For instance, when trying to split $340 equally among 10 people, you immediately know each person gets $34 since 340 is divisible by 10.
In Summary
The rule of 10 is a straightforward divisibility rule that states: a number is divisible by 10 if its last digit is 0. This provides a simple way to quickly assess if a number is a multiple of ten without carrying out long divisions.
