digital root

What is digital root in math? Definition

Digital root, also known as the repeated digital sum, is a mathematical concept that involves reducing a number to a single-digit value by summing its digits. This process is repeated until a single-digit number is obtained, which is known as the digital root of the original number.

History of digital root

The concept of digital root can be traced back to ancient times. It has been used in various cultures and civilizations, including ancient India and China. In India, it is known as "casting out nines," while in China, it is referred to as "casting out elevens." The digital root has also been studied by mathematicians such as Pythagoras and Fibonacci.

What grade level is digital root for?

Digital root is a concept that can be introduced at the elementary school level, typically around grades 4 or 5. It helps students develop their number sense and understanding of the properties of numbers.

What knowledge points does digital root contain? And detailed explanation step by step.

Digital root involves several knowledge points, including:

1. Place value: Understanding the value of each digit in a number.
2. Addition: Adding the digits of a number to obtain the sum.
3. Repeated addition: Continuously adding the digits until a single-digit number is obtained.
4. Number properties: Recognizing patterns and properties of numbers.

To find the digital root of a number, follow these steps:

1. Write down the given number.
2. Add all the digits of the number.
3. If the sum is a single-digit number, it is the digital root.
4. If the sum is a multi-digit number, repeat steps 2 and 3 until a single-digit number is obtained.

For example, let's find the digital root of the number 456:

1. 4 + 5 + 6 = 15
2. Since 15 is not a single-digit number, we repeat the process.
3. 1 + 5 = 6

Therefore, the digital root of 456 is 6.

Types of digital root

There are no specific types of digital root. The concept remains the same regardless of the number or its properties.

Properties of digital root

Digital root exhibits several interesting properties:

1. Invariance under permutation: The digital root of a number remains the same regardless of the order of its digits.
2. Congruence property: The digital root of a number is congruent to the number itself modulo 9.
3. Multiplicative property: The digital root of a product is equal to the digital root of the digital roots of the factors.

How to find or calculate digital root?

To find or calculate the digital root of a number, follow the step-by-step process mentioned earlier. Add the digits of the number until a single-digit number is obtained.

What is the formula or equation for digital root?

The digital root of a number can be expressed using the modulo operation. Let's denote the digital root of a number n as dr(n). The formula for calculating the digital root is:

dr(n) = (n - 1) % 9 + 1

How to apply the digital root formula or equation?

To apply the digital root formula, substitute the given number into the equation and perform the calculations. The result will be the digital root of the number.

For example, let's find the digital root of 789 using the formula:

dr(789) = (789 - 1) % 9 + 1 = 788 % 9 + 1 = 5 + 1 = 6

Therefore, the digital root of 789 is 6.

What is the symbol or abbreviation for digital root?

There is no specific symbol or abbreviation for digital root. It is commonly denoted as "dr(n)" or simply referred to as the digital root of a number.

What are the methods for digital root?

The main method for finding the digital root is by repeatedly summing the digits of a number until a single-digit number is obtained. However, the formula mentioned earlier provides a more efficient way to calculate the digital root.

More than 3 solved examples on digital root

Example 1: Find the digital root of 12345. Solution: 1 + 2 + 3 + 4 + 5 = 15 1 + 5 = 6 The digital root of 12345 is 6.

Example 2: Find the digital root of 987654321. Solution: 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 45 4 + 5 = 9 The digital root of 987654321 is 9.

Example 3: Find the digital root of 111111. Solution: 1 + 1 + 1 + 1 + 1 + 1 = 6 The digital root of 111111 is 6.

Practice Problems on digital root

1. Find the digital root of 987654.
2. Calculate the digital root of 24681357.
3. Determine the digital root of 999999.

FAQ on digital root

Question: What is the digital root of zero? Answer: The digital root of zero is zero itself.