10 little monkeys jumped on the bed, and one fell down and broke his head! Oh, that must have hurt for sure. So, how many of them are in good condition? Why were we taught this? The answer is pretty simple, to know and understand numbers. But why is knowing it important? This is what is going to be covered in this article. What is known as number system aptitude? Is number system important for aptitude? Let us look into these and more.
1. What is Number System Aptitude?
Photo by Susan Holt Simpson on UnsplashFrom childhood, humans are taught things, and numbers are one of the most important topics taught to us. Numbers are the mathematical values used for measuring, counting, or labelling objects. A number system goes further and is known to be defined as a system of writing for expressing numbers. Moving on to the other word which is aptitude, a competence to do a specific kind of work to a certain level or extent is what this is defined as.
If put together, the notation for being able to represent numbers of a set using symbols or digits and the ability of someone to do this to a certain level is what can be understood from the term number system aptitude. (See How much is 300 million in numbers?)
2. Is Number System Important for Aptitude?
If one is to ask -is number system important for aptitude, the answer is yes. Number system aptitude is defined as the ability of an individual to perform tasks which require working with numbers and data. The ratio for this can be considered rationally proportional which means that if a person has a high number system aptitude, they better will their performance in working with complex computations, numbers, and analysing data but at the same time if a person has a low number system aptitude then it would be the exact opposite and they would not be able to perform complex tasks including numbers and computations.
3. What are the Topics in Number System Aptitude?
Number system aptitude is a necessary subject in any and every situation and the important topics that come under this are as follows:
- Face value: This is defined as the actual value of the digit. No matter where the particular digit is placed, its value of it is never changed. For instance, if you take the number 526, then the face value of 2 is 2 no matter where it is.
- Place value: When the position of a digit in a number defines its value, it is known as place value. In short rather than the digit, its place is valued. Taking the same number 526, the place value of 6 is 6, 2 is 20, and 5 is 500 since those numbers are at their unit, tenth, and hundred places.
- Divisibility rules: This is known as the rules or test which helps one know if a number is divisible by another number without the actual division method.
4. What are the Number Aptitude Questions?
As discussed above, number system aptitude is defined as the ability of an individual to perform tasks which require working with numbers and data. Number aptitude questions often comprise of the following which are numbers, averages, problems on ages and clocks, simple and compound interest, time and work, profit and loss, speed, distance, time, percentages and ratio, pipes, partnerships and calendars, boats, streams, height, distance, perimeter, problems on trains and more. Some examples are as follows:
Example 1: Brad started a business with a capital of Rs. 80000. After 6 months Tim joined as a partner by investing Rs. 65000. After one year they earned a total profit of Rs. 20000. What is Tim’s share in the profit?
Option a. Rs. 5222.2
Option b. Rs. 5777.7 (correct answer)
Option c. Rs. 6222.2
Option d. Rs. 6777.7
Example 2: The speed of a boat in still water is 5km/hr. If the speed of the boat against the stream is 3 km/hr, what is the speed of the stream?
Option a. 1.5 km/hr
Option b. 2 km/hr (correct answer)
Option c. 2.5 km/hr
Option d. 1 km/hr
5. How do You find Aptitude Answers?
There are tons of websites where one can find aptitude questions and needless to say they have answers with them as well which are thoroughly explained so that it is not difficult for the target audience to understand them. Aptitude tests are pretty common and for reference, there are many types of tests which have specific questions and answers provided to help, learn and ace the test. (See Why is Mathematical Concept Important?)
6. What are Basic Number Systems?
Photo by Mika Baumeister on UnsplashNumbers are the mathematical values used for measuring, counting, or labelling objects. A number system goes further and is known to be defined as a system of writing for expressing numbers. The number system is used to represent a useful set of numbers which reflect the algebraic and arithmetic structure of a number. Some types of number systems are given below:
- Decimal number system: In this, every digit in a number has a specific place with a place value that it receives. This goes from right to left by starting with units and then moving on to tens, hundreds, thousands, and so on. For instance, 15367 has place values 10000 + 5000 + 300 + 60 + 7.
- Binary number system: This type of number system has a base value of 2 which means that it uses two digits which are 0 and 1 for the creation of numbers. This is useful and is used in computer systems and electronic devices.
- Octal number system: The base value of the octal number system is 8 as the name suggests. It uses numbers from 1 to 7 for the creation of its numbers.
- Hexadecimal number system: Lastly is the system with a base value of 16. 0 to 9 are taken as decimals but 10-15 are represented using alphabets A-F. So it goes like 0 1 2 3 4 5 6 7 8 9 A B C D E F.
7. What is the Purpose of Learning Number Systems?
Numbers are very important because to measure or quantify anything we use numbers. Even to check the time numbers come into play. When the representation of numbers is done using certain digits or symbols, they form a number system. So in short, a system that can be used to define a set of values which go on to represent a quantity is known to be a number system which plays a major role in our lives.
Hence, the purpose of learning number systems, taught to us since we were kids, is for us to understand and recognise numbers and at the same time to differentiate and compare them to make sense in quantifiable and comparative terms. Check out How can You Find the Sum of the First 100 Natural Numbers?
8. How do You Study Number System?
Studying the number system can be a difficult task but as we are brought up from childhood with this so it doesn’t feel like much of a task. Some steps to help with this are as follows:
- Teaching counting with number rhymes: You might have heard of 10 little monkeys jumping on the bed or 1 2 buckle my shoes! These were rhymes taught to children so that it is fun and at the same time informative as they are learning in the process.
- Write numbers and draw the quantity: By writing the number and drawing the quantity beside it, the whole concept becomes easier to understand because of these visual aids and interactive skills, all in one.
- Vehicles and ad boards: Pointing out numbers on vehicle number plates, ad billboards, and posters and reading them out can be considered as an exercise to improve the number system concept to anyone.
- Connect the dots using numbers: You might have done fun activities such as connecting the dots to draw something out and when these are done with numbers, the whole sequence is understood better.
- Counting toes and fingers: The most basic and at the same time useful technique is used wherein one counts their toes and fingers on hands and legs because this helps in introducing counting anywhere and practising on a daily basis helps with understanding it better.
9. What is the Formula of Number System?
Photo by Antoine Dautry on UnsplashThere are many types of formulas for number systems and a few which are considered important are jotted down:
- 1 + 2 + 3 + 4 + 5 + … + n = n(n + 1)/2
- (1^{2} + 2^{2} + 3^{2} + ….. + n^{2}) = [n ( n + 1 ) (2n + 1)]/6
- (1^{3} + 2^{3} + 3^{3} + ….. + n^{3}) = [n(n + 1)/ 2]²
- Sum of first n odd numbers = n²
- Sum of first n even numbers = n (n + 1)
- (a + b)(a − b) = (a² – b²)
- (a + b)² = (a² + b² + 2ab)
- (a − b)²= (a² + b² − 2ab)
- (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
- (a³+ b³) = (a + b)(a² − ab + b²)
- (a³ − b³) = (a − b)(a² + ab + b²)
- (a^{3}+ b^{3} + c^{3} − 3abc) = (a + b + c)(a^{2} + b^{2} + c^{2} − ab − bc − ac)
- When a + b + c = 0, then a_{3} + b_{3} + c_{3} = 3abc
Hope this helped with understanding the significance of numbers and answering questions such as whether is number system important for aptitude and also what is known as number system aptitude. (Also read How to do Addition using Standard Algorithm?)