Digits in our Daily Use
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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
FAQs on Digits
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 is 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.
3. What is the difference between digit and number?
Digit is any of the symbols from 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For example, 100 is a three-digit number, 10 is the ten-digit number and 1 is a single-digit number.
On the other hand, a number can be a series of digits or alphanumeric digits. It can be written with a single digit or a combination of digits.
For example, if someone asks for your number you will arrange 10 digits to give one phone number. Similarly, if someone asks for the car’s number then we will have a series of alphanumeric digits that will form the number of the car.
4. What is the importance of learning the digit system?
It is important to learn the digit system for the following reasons -
It helps in counting the numbers.
Digits help identify the one’s place, tenth place, hundredth, and the thousandth place.
It helps you to perform the mathematical functions of subtraction, addition, multiplication, and division.
Even the Romans used Roman numbers in writing format but for calculation even they use the abacus and the digits are formulated on the position of the abacus.
Thus, digits form the basis of all the mathematical calculations
5. What is the digit place of 1 billion in the number system?
This is the basic concept taught to the students as they start learning about digits in lower classes. Follow the list given below to understand the place value of different digits -
1 Unit place (Ones) Digit 1
10 Tens place (Tens) Digit 2
100 Hundredth place Digit 3
1000 Thousandth place Digit 4
10000 Tens of Thousandth Digit 5
100000 Hundreds of Thousandth Digit6
1000000 MillionsDigit Digit 7
1000000000 BillionsDigit Digit 10
So, the digit place of one billion is 10th place.
6. How many two digits numbers are there?
You should first try to get the answer by the process of counting manually. Start counting from the smallest two-digit number, which is 10 as 9 comes before 10 and it is a single-digit number. Identity the range by knowing the smallest three-digit number which is 100. 99 comes before 100 which is the highest two-digit number, so from 10 to 99 is the total number of two digits numbers. If you count, you will get the answer as 90.
Now, the simple way of doing it is from 1 to 100 there are 99 numbers minus the single digits number so we have, 99 - 9 = 90.
