If you are a math enthusiast, you must have come across the concept of divisibility. In layman’s terms, divisibility is the ability of a number to be evenly divided by another number without leaving any remainder. One of the simplest and most fundamental concepts in divisibility is the divisibility rule for 10. In this article, we will explore the basics of this concept, including how it works and why it is important.

## What is the Divisibility Rule for 10?

The divisibility rule for 10 states that any number ending in 0 is divisible by 10. In other words, if the units digit of a number is 0, then the number is divisible by 10. For example, 30, 140, 1000, and 5000 are all divisible by 10 because they end in 0. On the other hand, numbers like 34, 187, and 2021 are not divisible by 10 because they do not end in 0.

## How does the Divisibility Rule for 10 work?

The reason why the divisibility rule for 10 works is rooted in our base-10 number system. In base-10, we use ten digits, from 0 to 9, to represent any number. The position of each digit in a number represents a power of ten, with the rightmost digit representing the units place, the second-rightmost digit representing the tens place, and so on.

When we divide a number by 10, we are essentially removing the units digit from the number. For example, when we divide 345 by 10, we get 34.5. In other words, we are left with the number that represents the tens and higher places. However, when we divide a number ending in 0 by 10, we simply remove the 0 from the end of the number, leaving us with the number that represents the tens and higher places. Since 10 is a factor of 100 (10 x 10), any number that is divisible by 10 is also divisible by 100, 1000, and so on.

## Why is the Divisibility Rule for 10 important?

The divisibility rule for 10 is important because it is a foundational concept in number theory and serves as a building block for other rules of divisibility. For example, the divisibility rule for 2 states that any even number is divisible by 2, while the rule for 5 states that any number ending in 5 or 0 is divisible by 5. These rules are based on the fact that 2 and 5 are factors of 10. Therefore, understanding the divisibility rule for 10 is crucial for understanding other rules of divisibility.

Moreover, the divisibility rule for 10 is a useful tool for checking calculations and verifying answers. If you are multiplying or adding numbers and need to check whether the result is divisible by 10, you can simply check the units digit of the result. If it is 0, then the result is divisible by 10. This is especially useful in situations where you need to perform quick mental calculations or estimate answers.

## Examples of the Divisibility Rule for 10 in Action

Let’s look at some examples of how the divisibility rule for 10 can be applied in practice.

Example 1: Is 9,350 divisible by 10?

Solution: No, because the units digit of 9,350 is 0.

Example 2: Is 4,167 divisible by 10?

Solution: No, because the units digit of 4,167 is 7, not 0.

Example 3: Is 10,000 divisible by 10?

Solution: Yes, because the units digit of 10,000 is 0.

Example 4: Is 32,310 divisible by 10?

Solution: No, because the units digit of 32,310 is 1, not 0.

Example 5: Is 5,001 divisible by 10?

Solution: No, because the units digit of 5,001 is 1, not 0.

As you can see from these examples, applying the divisibility rule for 10 is a straightforward process that involves simply checking the units digit of a number.

## FAQs

### What is the difference between the divisibility rule for 10 and the rule for 2?

The divisibility rule for 10 states that any number ending in 0 is divisible by 10, while the rule for 2 states that any even number is divisible by 2. Both rules are based on the fact that 10 and 2 are factors of the base-10 number system.

### Can the divisibility rule for 10 be applied to decimals?

No, the divisibility rule for 10 only applies to whole numbers.

### Is the divisibility rule for 10 the only rule of divisibility?

No, there are many other rules of divisibility that apply to different numbers and factors.

### How can I use the divisibility rule for 10 in mental calculations?

By checking the units digit of a calculation, you can quickly determine if the result is divisible by 10.

### What is the importance of understanding the divisibility rule for 10?

Understanding the divisibility rule for 10 is important for building a foundation in number theory and improving your math skills. It is also a useful tool for checking calculations and verifying answers.

## Conclusion

In summary, the divisibility rule for 10 is a fundamental concept in divisibility that states any number ending in 0 is divisible by 10. It is based on our base-10 number system and is a crucial building block for other rules of divisibility. Moreover, it is a useful tool for checking calculations and verifying answers. By understanding and applying this rule, you can improve your number sense and math skills.