 # Digits

## Digits In Our Daily Use

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 problems are numbers. However, numbers are really 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. You must be wondering then what are those figures that we use to solve our mathematical problems? This is where “digits” make its grand entry.

### What are Numbers, Numerals and Digits?

Before we understand what are digits, remember, numbers are simply the idea of a measure of any countable object. In order 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 numerals and numbers, let us focus on the smallest mathematical units of our numeral systems; the digits. So, we know that numerals are the symbolic representations of numbers. But, what are numerals represented by? The answer is digits. Digits are the single symbols which 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 1 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 upto 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 which 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 placed under the tens place and the second under the ones 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 =90.

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 ones position, 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:

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

1. What is the Smallest One Digit Number?

The smallest one digit number is 1. This is because ‘0’, which many perceive as representing a smaller value than 1, actually does not have any value by itself. It is only when the digit 0 is placed on the right side of another digit that it adds value to the numeral. For example, if you write 022, the number is actually 22. That is because when you are 0 in itself has no value. Also, if you use the positioning theory, 022 might look like a three digit number. But if we place the numbers in HTO form:

HTO

022

Then, what it actually turns out is: 000+20+2. Since 0 has no value, the addition will mean 22 is the answer.

However, when placed after a number, the value of the number changes. 9 is nine and 09 is also nine but 90 is termed as ninety. The rule for this is simply positioning.

2. What is the Smallest 2 Digit Number?

We arrive at 2 digit numbers by adding another unit to the highest one digit number, which 9. The second unit that is added to the highest one digit number may vary but in order to derive the smallest 2 digit number, we need to add to it the smallest one digit number, which is 1. Therefore, The smallest 2 digit number would be calculated as 9+1 which will come up to 10.

This brings us to the question, how many 2 digit numbers are there? To answer that, if we start counting from 0 to the highest two digit number, which is 99, there are a total of ninety 2 digit numbers which start from 10 and count up to 99.