How to Find the Unit Digit of a Number
Understanding how to find the unit digit of a number is a vital concept in mathematics, especially when dealing with large numbers or exponents. Whether you’re tackling competitive exams or solving mathematical puzzles, knowing how to efficiently calculate unit digits is crucial.
In this article, we’ll explain how to find the unit digit of any given number using simple techniques, including remainder division and cyclicity patterns.
The unit digit is the rightmost digit of any given number, often referred to as the “ones place” or ones digit. For example, in the number 3451, the unit digit is 1.
The unit digit can be found using two primary methods: visual identification and calculation through patterns. Let’s explore each one.
For most numbers, the unit digit can be easily identified by simply looking at the number and focusing on the rightmost digit before the decimal point.
In some cases, especially when dealing with exponentiation, the unit digit follows a specific pattern or cycle. For instance, consider powers of 2:
This repeating cycle of 2, 4, 8, 6 helps us determine the unit digit for any exponent of 2.
Pro Tip: Identify the remainder when dividing the exponent by the length of the cycle. For example, to find the unit digit of 2^60, divide 60 by 4 (the length of the cycle). The remainder is 0, so the unit digit of 2^60 is 6.
Another efficient method to find the unit digit is by finding the remainder when a number is divided by 10. This approach is straightforward and works well with large numbers.
For example:
Let’s look at some practical examples to better understand how to calculate the unit digit.
Problem: Find the unit digit of the product 684 × 759 × 413 × 676.
Solution: The unit digit of the product is determined by multiplying the unit digits of each number:
Now, calculate the product of the unit digits:
4 × 9 × 3 × 6 = 648
The unit digit of 648 is 8, so the unit digit of the entire product is 8.
Problem: Find the unit digit of (3547)^153 × (251)^72.
Solution:
Now, using the pattern for powers of 7, we know the cycle is 7, 9, 3, 1.
Hence, the unit digit of the product is 7 × 1 = 7.
Conclusion
By mastering these methods, you’ll be able to quickly and accurately find the unit digit of any number, whether it’s a large product, a sum, or an exponentiation.