What is the Test for Divisibility by 10?

S3-SA4-0045

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The test for divisibility by 10 helps us quickly check if a number can be divided by 10 without leaving any remainder. A number is divisible by 10 if its last digit, also known as the digit in the 'ones place', is a zero.

Simple Example

Quick Example

Imagine you have a stack of 250 ₹10 notes. Can you divide them equally among 10 friends? Yes, because 250 ends with a 0. Each friend would get 25 notes. If you had 253 notes, you couldn't divide them equally among 10 friends, as 253 does not end in 0.

Worked Example

Step-by-Step

Let's check if the number 7890 is divisible by 10.

1. Look at the last digit of the number 7890.
2. The last digit is 0.
3. According to the divisibility rule for 10, if the last digit is 0, the number is divisible by 10.
4. So, 7890 is divisible by 10.

Answer: Yes, 7890 is divisible by 10.

Why It Matters

Understanding divisibility rules helps in quickly simplifying calculations, which is crucial in fields like Computer Science for efficient programming or in Data Science for organizing large datasets. Engineers use these rules for quick estimates, and even in Cryptography, understanding number properties is fundamental for creating secure codes.

Common Mistakes

MISTAKE: Thinking any number with a 0 somewhere in it is divisible by 10 (e.g., 105). | CORRECTION: Only the *last* digit (the ones place) must be 0 for a number to be divisible by 10. 105 is not divisible by 10 because its last digit is 5, not 0.

MISTAKE: Confusing divisibility by 10 with divisibility by 5 (where the last digit can be 0 or 5). | CORRECTION: For divisibility by 10, the last digit *must* be 0. For divisibility by 5, it can be 0 or 5.

MISTAKE: Not checking the ones place correctly, especially in large numbers. | CORRECTION: Always focus only on the very last digit of the number, no matter how many digits the number has.

Practice Questions

Try It Yourself

QUESTION: Is 450 divisible by 10? | ANSWER: Yes

QUESTION: Which of these numbers is NOT divisible by 10: 120, 305, 780, 900? | ANSWER: 305

QUESTION: A shopkeeper is packing ₹10 pens into boxes. Each box must contain a number of pens that is divisible by 10. If he has 175 pens, can he pack them all into such boxes without any pens left over? | ANSWER: No, because 175 is not divisible by 10 (its last digit is 5).

MCQ

Quick Quiz

Which of the following numbers is divisible by 10?

123

450

675

892

The Correct Answer Is:

A number is divisible by 10 if its last digit is 0. Only 450 has 0 as its last digit. The other numbers end in 3, 5, or 2, so they are not divisible by 10.

Real World Connection

In the Real World

When you buy items at a local kirana store and the total bill comes to, say, ₹340, you know you can easily pay with ₹10 notes or ₹100 notes because 340 is divisible by 10. This makes handling money and giving change simpler in everyday transactions, especially with digital payments like UPI where exact amounts are common.

Key Vocabulary

Key Terms

DIVISIBILITY: The ability of one number to be divided by another number without a remainder. | REMAINDER: The amount left over after division. | ONES PLACE: The rightmost digit in a whole number. | DIGIT: A single symbol used to make numbers (0, 1, 2, 3, 4, 5, 6, 7, 8, 9).

What's Next

What to Learn Next

Great job learning about divisibility by 10! Now that you know this, you can easily move on to understanding divisibility by 2 and 5, as these rules are closely related and build on similar concepts about the last digit of a number.