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𝐂𝐨𝐮𝐧𝐭𝐢𝐧𝐠 𝐍𝐮𝐦𝐛𝐞𝐫 𝐢𝐬 𝐛𝐢𝐚𝐬𝐞𝐝?

In today's world, there are mainly three systems of counting:
1) Base 10
2) Base 2 (Binary)
3) Base 16 (Hexadecimal)

Base 10:
This system is what we use to count in every day life. One apple, Three people, Seventy-six dolphins, etc.
It consists the digits {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

Base 2:
Base 2 system only consists 0 and 1. Computers use 0 and 1 to represent off and on respectively. The ascending order of numbers would go as follows: 0, 1, 10, 11, 100, 101, 110, 111, etc.

Base 16:
Similarly to Base 10, when we reach till the number 9, we move on by using "alphanumeric numbers" which is just a, b, c, d, e and f. So the whole sequence would be {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f}. a would represent 10, b would be 11, c would be 12, and so on.

It is clear that base 10 system is popular because humans have 10 fingers and when we want to count more than 0 to 9, we re-use the digits to make up more numbers such as 10, 11, 12, ... But what if we had 11 fingers? Instead of using two digits 1 and 1, we would have created a new one-digit number. Or what if we had 20 fingers, instead of writing it as 2 and 0 we would represent it as an another one-digit number.

This concludes my point that if we ever meet any extraterrestrial life outside Earth and they happen to have more than 10 fingers, there's no doubt we will have a new counting system with new numbers (or will they even be "numbers"???).

Fun fact: In every counting system, when the last digit ends (after 9 (base 10), after 1 (base 2) and after f (base 16) ), all of them continue as the number "10". ;)

S. W. A. N.
For Class Requests:
WA: +6584177507

What is "𝑒"?
"𝑒" also known as "Euler's Number" is derived from the equation of 𝙲𝚘𝚖𝚙𝚘𝚞𝚗𝚍 𝙸𝚗𝚝𝚎𝚛𝚎𝚜𝚝, 𝐀 = 𝐏(𝟏 + 𝐫/𝐧)^𝐧
where A = amount after n compounding periods,
P = principal (original amount)
n = the number of compounding periods.

As n (the number of times you compound the interest) becomes larger and larger, the limit approaches 𝑒 (as shown in image below).

n→∞ (1 + 1/n)^n = e ≈2.718281828.
lim

Why is "𝑒" important?
- It appears in many areas of mathematics, including calculus, complex numbers, probability theory, and number theory.
- It is the base of natural logarithms, making it crucial in solving exponential growth problems.
- In physics, e appears in descriptions of natural phenomena, such as radioactive decay, population growth, and heat transfer.

For IGCSE Mathematics classes application
WA: +6584177507

𝐇𝐨𝐰 𝐭𝐨 𝐠𝐞𝐭 𝐛𝐞𝐭𝐭𝐞𝐫 𝐚𝐭 𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐬? 🤓💭
I've received many questions asking how to improve their mathematical skills and knowledge. Today, I will sharing MY top 3 advices to take your maths to the next level.
𝟏.) 𝐃𝐨𝐧'𝐭 𝐛𝐞 𝐚𝐟𝐫𝐚𝐢𝐝 𝐨𝐟 𝐌𝐚𝐭𝐡𝐞𝐦𝐚𝐭𝐢𝐜𝐬. A lot of people will struggle to believe that the reason why they are less motivated to do maths questions are because they're intimidated by them. So, the first stepping stone would be to take on any challenges even if it's extremely difficult.
𝟐.) 𝐀𝐬𝐤 𝐲𝐨𝐮𝐫 𝐭𝐞𝐚𝐜𝐡𝐞𝐫/𝐭𝐮𝐭𝐨𝐫. When you have found the courage to solve hard questions, most of the times you won't be able to figure out answers without a little help from none other than the people who taught you maths. (And for tutor help, don't forget to pm Swan Tutors! ;) )
And last but not least,
𝟑.) 𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐞. 𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐞. 𝐏𝐫𝐚𝐜𝐭𝐢𝐜𝐞. Mathematics is a tool not a subject. You need many "hands-on" experiences to learn as you go. Isaac Newton wouldn't have found out about the gravity if the apple actually hadn't have fallen on him. Fleming wouldn't have created penicillin if he didn't let it set over his holidays.
For more content like these and fun facts about Maths, make sure to give it a follow AND for any tutor request please contact WA: 84177507.
Hope you have a pleasant day

𝐑𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫𝐬 𝐯𝐬 𝐈𝐫𝐫𝐚𝐭𝐢𝐨𝐧𝐚𝐥 𝐍𝐮𝐦𝐛𝐞𝐫𝐬

- What are rational numbers?
Rational numbers are numbers that can be written as a ratio of two integers in which denominator should not be zero.
In simpler words, any full numbers, integers, fractions are a part of rational numbers.
For example: 0,1, 2/3, -12, 0.36
Note: Any decimal part must terminate or resolve into a repeating pattern

- What are irrational numbers?
Irrational numbers are all real numbers that aren't rational numbers. We all know one famous irrational number which is pi (π) and its value 3.14159265359....
And it is an irrational number because the decimal part never repeats in pattern nor has an end.
For example: -√3, π, -0.23691847.....

- Why do we need to know this?
Whilst encountering mathematical sums, it is important to know that the answer you have concluded to makes sense or not. And only if you see and acknowledge an irrational number, you will realize the sum does not have an answer or it's an error.

For more details,
WhatsApp: 8417 7507
Email: [email protected]

Hello Everyone! I’m Swan Zayar, the founder of “Swan Tutors” and welcome to my page.
For those of you who don’t know me yet, I’m going to briefly explain about who I am and what I offer.

I’m a CIE IGCSE ‘O’ Level (Oct/Nov) graduate currently attending a Foundation Year program. Since I was in Grade 5, I’ve taken a ton of Maths Olympiads exams and achieved many Gold, Silver, and Bronze medals.
So today, I have decided that I will be sharing my knowledge of Maths with you by starting the page, “Swan Tutors”.