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Mathematics is a very interesting subject. Some love it while others fear it. From different tricks and tips, mathematics lays down a number of amazing facts to help students get involved with this subject in a better way. In this article, we are listing down 10 amazing facts about numbers.

## Amazing Facts About Numbers in Maths

These are some of the amazing facts about numbers in maths.

### 1. There are more ways to arrange a deck of cards than there are atoms on Earth

The first in our list of interesting facts about numbers is about the arrangement of 52 cards in a deck. This is the thing that you won’t believe. But it’s true. The fact is that if you shuffle a deck of cards, it’s likely that exact order never existed before in the history of the universe!

A deck of 52 cards can be shuffled in 8 × 10^{67} ways. Let’s see how I arrive at this number.

Number of cards in a deck = 52

Therefore, the number of ways these 52 cards can be arranged = ^{52}P_{52} = 52!/(52 – 52)! = 52!/0!

= 52!/1 = 52 × 51 × 50 × … × 1 = 8.1 × 10^{67}

To put that in, even if someone could rearrange a deck of cards every second of the universe’s total existence, the universe would end before she/he would get even one billionth of the way to finding a repeat.

One billionth of the total number of ways the cards can be arranged = (8.1 × 10^{67})/(1 billion)

= (8.1 × 10^{67})/(10^{9}) = 8.1 × 10^{58} ways

Time required = 8.1 × 10^{58} seconds = 2.6 × 10^{51} yearsThe life of the universe is 13.8 billion years = 4.4 × 10^{17} seconds.

### 2. The Fibonacci Sequence appears in nature

Leonardo Fibonacci lived in the 13th century in Italy. He is credited with discovering a mathematical sequence that’s now named after him – the Fibonacci Sequence. The Fibonacci sequence is one of the most interesting number facts in the universe. Starting at 0 and 1, this sequence is generated as the sum of two preceding numbers in the sequence. The sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The Fibonacci Sequence often appears in nature –

- Petals in flowers
- Fibonacci spirals are found in sunflowers, daisies, cauliflower, snails, sea shells, waves
- Organs of the human body
- In music
- Pascal’s triangle
- Organs of dolphin
- In DNA (Deoxyribonucleic acid)

### 3. There’s not enough room in the world to write out a Googolplex

The next interesting number facts are about the two extremely large numbers that one cannot even imagine. Yes, we are talking about the numbers googol and googolplex.

If you start to write googolplex and print it out in a volumized series of books, it would weigh more than the entire planet.

A googol means 1 followed by 100 zeroes. A googolplex is 1 followed by a googol zeros.

1 googol = 10^{100}

1 googolplex = 10^{10^100}

Assuming that a single digit needs 1 sq millimetre (10^{-6} sq metre) of space, then 10^{10^100} many digits will need (10^{10^100}×10^{-6}) sq metre of space.

And it will require (10^{10^100}×10^{-6})/(6.2 × 10^{-2}) = (10^{10^100}×10^{-4})/6.2 sheets of A4 size paper (Size of 1 A4 size paper = 6.2 × 10^{-2} sq metre

Thus, the weight of the paper required = ((10^{10^100}×10^{-4})/6.2) × 5×10^{-3} kg = 10^{10^100}×8.1×10^{-8} kg (Weight of 1 A4 size paper = 5 gram)Compared to this weight, the whole solar system weighs much less. (Weight of solar system = 2.0028 ×10^{30} kg)

### 4. Easy way to multiply a number by 12

The next in our list of interesting facts about numbers relate to the multiplication of numbers. Most of you might be knowing a shortcut to multiplying a number by 11. It is done by keeping the first and last digits as it is and the remaining digits are obtained by adding the adjacent digits starting from the right.

e.g., 2336 × 11 = 2 (2 + 3)(3 + 3)(3 + 6) 6 = 25696

A similar method can be used to multiply any number by 12. Consider multiplying 3212 by 12.

**Step 1:** Stuff the number between two 0s. 3212 → 032120

**Step 2:** Starting from the right and taking two digits at a time, add the right digit with the twice of next digit

032120 → (2×0 + 3)(2×3 + 2)(2×2 + 1)(2×1 + 2)(2×2 + 0) = 38544

The same process can be used to multiply a number by 13. (Instead of adding twice the next digit, add thrice the next digit).

Let’s multiply 3212 by 13

032120 → (3×0 + 3)(3×3 + 2)(3×2 + 1)(3×1 + 2)(3×2 + 0) = (3)(11)(7)(5)(6) = 41756 (1 in 11 is carried forward and added with 3 next to it).

Can you extend this method to multiply a number by 14 or 15?

### 5. You can actually reach the moon by folding a piece of paper of 0.01 mm 45 times

Yes, you read it right. For this, you have to use some mathematics. This is yet another interesting number facts about numbers. For this consider the following scenario.

Initially, we have a paper that is 0.01mm thick. If we fold the paper once, it is now 0.02 mm in thickness. If we fold it one more time, it is now 0.04 mm thick. If we fold it one more time, it is now 0.08 mm thick. Did you notice the pattern? Every time we fold the paper it gets twice as thick.

If we fold this paper 17 times we’ll get a thickness of 2 to the power of 17, which is 131cm and that equals just over 4 feet. (Thickness of paper = 2^{17} × 0.01 mm = 2^{17} × 0.01 × 0.1 cm = 131.072 cm)

If we were able to fold it 25 times, then we would get 2 to the power of 25, which is 33,554 cm and that equals over 1,100 feet. It’s worthwhile to stop here and think for a moment. Folding a paper in half, even a paper so thin, 25 times would give us a paper almost a quarter of a mile.

This type of growth is called Exponential Growth. If we fold a paper 30 times, the thickness reaches 6.67 miles which is about the average height that planes fly.

40 times, the thickness is nearly 7000 miles or the average GPS satellite’s orbit. 45 times, the thickness is now over 250,000 miles and the distance between the earth and the moon is around 239,000 miles. So we finally reached the moon.

And by folding it one more time i.e. 46th time we can now come back to earth!!

### 6. What comes after a million, billion, and trillion?

You have been using the terms like million, billion, or trillion to represent very big numbers. Have you ever wondered what we can call numbers bigger than these?

You can term these numbers as quadrillion, quintillion, sextillion, septillion, octillion, nonillion, and decillion.

$1 \text{ million } = 10^{6}$ | $1 \text{ billion } = 10^{9}$ | $1 \text{ trillion } = 10^{12}$ |

$1 \text{ quadrillion } = 10^{15}$ | $1 \text{ quintillion } = 10^{18}$ | $1 \text{ sextillion } = 10^{21}$ |

$1 \text{ septillion } = 10^{24}$ | $1 \text{ octillion } = 10^{27}$ | $1 \text{ nonillion } = 10^{30}$ |

$1 \text{ decillion } = 10^{33}$ |

### 7. Most mathematical symbols weren’t invented until the 16th century!

One cannot think of mathematics without its symbols. And the next in the list of amazing facts about numbers is related to the mathematical operators that we use to add, subtract, multiply and divide. We are used to symbols like $+$, $-$, $\times$, and $\div$ are used frequently. Will you believe that all these symbols were discovered very recently? Most of the mathematical symbols weren’t invented until the 16th century. Before that, people used to write equations in words.

Robert Recorde, the designer of the equals sign, introduced plus and minus to Britain in 1557 in The Whetstone of Witte.

The multiplication sign was obtained by changing the plus sign into the letter $\times$. This was done because multiplication is a shorter form of addition.

The division was formerly indicated by placing the dividend above a horizontal line and the divisor below. In order to save space in printing, the dividend was placed to the left and the divisor to the right. After years of evolution, the two “ds” were omitted altogether and simple dots were set in the place of each.

### 8. Is it “math” or “maths”?

The next in our list of interesting facts about numbers is the word ‘math’ itself. If you’ve grown up using the word math, you might be wondering about the word maths, which you’ve probably encountered from time to time. The same goes, of course, if you grew up saying maths? Do you think it is a typographical error? If not, then which one is correct?

Both math and maths are short for the word mathematics.

The word math can refer to either the discipline or subject of mathematics. It can also refer to mathematical procedures. In a sentence like ** She enjoys studying math and science**, the word math refers to the subject or discipline of mathematics. In the sentence

**, math refers to actual calculations.**

*She insisted on seeing his math so she could understand his proposal*Maths has the very same definition as math. If you substitute maths into any of the above examples, the sentences mean the exact same thing. For example, *He loves school, but he especially enjoys maths.*

The only difference between math and maths is where they’re used. Math is the preferred term in the US and Canada. Maths is the preferred term in the UK, Ireland, Australia, and other English-speaking places.

### 9. Temperature of -40 is the same in Celsius and Fahrenheit

The degree of hotness or coldness of a body i.e., the temperature is commonly measured in either Celsius or Fahrenheit. These two scales follow different scales to measure the temperature.

Our next in the list of amazing facts about numbers is related to these two scales of measurement.

For example, The temperature of $25^{\circ} \text{C}$ is the same as that of $77^{\circ} \text{F}$ and $-30^{\circ} \text{C}$ is the same as that of $-22^{\circ} \text{F}$.

But there is one temperature point where both scales have the same reading. And that is $-40$.

$-40^{\circ} \text{C } = -40^{\circ} \text{F}$

Why is it?

The formula used for the conversion of temperature between Celsius and Fahrenheit is

$\text{C }= \frac{5}{9}\times \left(F – 32 \right)$ or $\text{F} = \frac{9}{5} \times \text{C} + 32$

When $\text{F }= -40$, then $\text{C }= \frac{5}{9}\times \left(-40 – 32 \right)$

$ = \frac{5}{9} \times \left(-72 \right) = 5 \times \left(-8 \right) = -40$

When $\text{C }= -40$, then $\text{F }= \frac{9}{5} \times \left(-40 \right) + 32 $

$= 9 \times \left(-8 \right) + 32 = -72 + 30 = -40$

### 10. Prime numbers protect us from cyber crimes

You might not be aware, but prime numbers keep our accounts and information safe. Namely, through the RSA encryption system. RSA encryption was invented in 1978 by Ron Rivest, Adi Shamir, and Leonard Adleman. The encryption system combines simple, known facts about numbers to secure the transfer of information—such as credit card numbers – online. The encryption algorithm is based on two large prime numbers.

Another among the list of amazing facts about numbers is related to prime numbers. Prime factorization can be extremely hard with bigger values, and as such, the unique factors of two large primes are not that easy to crack, which protects users’ data.

## Practice Problems

- What are Fibonacci numbers?
- What are prime numbers?
- What are composite numbers?
- What is the formula to convert temperature from Celsius to Fahrenheit?
- What is the formula to convert temperature from Fahrenheit to Celsius?

## Conclusion

These were some of the amazing facts about numbers. Numbers play an important role in our lives. We use numbers frequently even without realizing it. There are many numbers and their sequences which exhibit interesting patterns.

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