[Maths Class Notes] on Digits Pdf for Exam

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When we think of a house, we usually imagine a group of people living under the same roof, the interior decor, and the overall domestic experience. But in reality, a house is a building erected with brick and mortar. The relationship between digits and mathematics is similar to this. The building blocks of any mathematical problem are numbers. However, numbers are the idea of a certain measure. For instance, if we see five houses next to each other, our brains will tell us that the number of houses that we see is five, even without it explicitly written anywhere. This is where “digits” make their grand entry. 

Let us learn in detail about the concept of digits in this article.

What are Numbers, Numerals and Digits?

Before we understand what digits are, remember, numbers are simply the idea of a measure of any countable object. To depict numbers, we use certain standardised symbols which are called numerals. So, those who are familiar with the roman numeral system will understand that “IV” stands for the number four. The most frequently used numeral system is the decimal system which comprises the numerals 1,2,3,4,5,6,7,8,9,0. These symbols are combined in different formats to denote various ‘numbers’. For instance, numerals 200 represents the number two hundred. 

Now that we have established the difference between numerals and numbers, let us focus on the smallest mathematical units of our numeral systems; the digits. So, we know that numerals are symbolic representations of numbers. But, what are numerals represented by? The answer is digits. 

Digits are the single symbols that combine to make up a numeral which in turn represents the number. Digits can by themselves stand for singular numerals like “5” as both a digit and a numeral representing the number five. Two or more digits can combine to denote numerals of larger values like “5” and “2” will represent 52 or the number fifty-two. 

How did the Digits Come to be?

Mathematics as a discipline revolves around counts or values. In ancient times, people would use tangible objects like stones to depict a measure. Eventually, it became necessary to develop a more logical and sustainable method for greater values. This is why the digit system was developed. 

Types of Digits and Numbers

The digits combine in different permutations to portray different numbers. You may be thinking to yourself, how many one digit numbers are there? Typically, there are ten digits in the decimal number system, starting from 0 and counting up to 9. In the decimal number system, the smallest one-digit number is 1. 9 is the highest one-digit number. Therefore to answer the question, how many one-digit numbers are there;, there are ten one-digit numbers including 0. The decimal system goes up to infinity since there can be endless combinations of the ten digits to come up with a particular numeric value. So, while we can conclusively say what the smallest one-digit number is, there is no answer to the question, ‘what is the highest number in the decimal system?’

If we wish to represent a value that is higher than the one-digit numbers, for instance, the number of students in a class, then, we take the help of two-digit numbers. If we add another unit to the highest one-digit number, we arrive at the smallest two-digit number.

For example, 9+1=10

Similarly, 7+7 = 14

So, by placing one digit in the tens place and another in the units place, you get 2-digit numbers.

The highest two-digit number is 99. In a two-digit number, the first number is placed under the tens place and the second under the one’s place.

TO

99

Under T or tens, we place the digit 90 and then we add the ‘ones’ digit 9 with the previous one. 90+9 =99.

If we write three-digit numbers, like 155 we have three positions, Hundreds, Tens and Ones.

HTO

155

Under the hundredth position, we place the 100, under the Tens position, we place 50 and under the position of the one, we place 5. Thus, 100+50+5 = 155. The largest 3-digit number is 999.

The positioning rule can be applied for 4-digit numbers, 5-digit numbers, to infinity.

Solved Example:   

Find the total numbers of three-digit numbers, which are exactly divisible by six?

Solution:

The total number of 3-digit numbers from 100 to 999 is 900.

Therefore, the least 3-digit number divisible by 6 is 6 × 17 = 102 and greatest number is 6 × 166 = 996.

Therefore, required number of numbers = 166 – 17 + 1 = 150