**The Magic of Number 9**** **

**1.****F**inding the Digital Roots by Casting 9

**What is Digital root?**

If we add up the digits of a number until there is only one number left we have found what is called the digital root. In other words, the sum of the digits of a number is called its digital root.

** Example: **

For 5674, 5 + 6 + 7 + 4 = 22 and 2 + 2 = 4

» 4 is the digital root of 5674

One use of digital roots is for divisibility tests (like 3 and 9). This method makes it easier to calculate the digital root.

**Example: **

**Example: **

Find the digital root of 257520643

**Steps:**

1.2 + 7 = 9, cross out 2 and 7.

2.4 + 3 = 9, cross out 4, 3 and 2.

3.There are no other groups of numbers adding up to 9.

4.Add up the remaining digits, 5 + 5 + 0 + 3 = 13.

5.13 is more than 9, so 1 + 3 = 4.

6.The digital root is 4.

If there is nothing left after having cast out nines then the digital root is 9.

**2. I do not like him, why does he follow me? **

In the nine times table below notice that the digits of each product sum to nine. Why does this happen? Look at how the digits of the product are changing each time.

I would like to tell the class that due to some reason (Purani dushmani) I do not like No. 9, so to get rid of him I multiply him by 5, we get 45 which is 4 + 5 = 9 then, I look skywards, roll my eyes, and say oh oh he has come again!

Then I say ok let me multiply him by 7. The experience repeats. By this time the students have caught on and want me to multiply by 8, by 9, by 15, and so on.

**3. Inverse Table**

Write the multiplication table of 9 and interchange the place value of every number obtained. Observe the pattern. How fascinating it is!

Do you think this will work for the table 8? Try!

**4. Snake eats its own tail **

Think of a two digit number, say 42, then subtract the reverse of its digits, 24, from 42

Choose any two digits number and for each one reverse the digits and subtract the smaller number from the larger. Look at all the answers you get. Do they all have a common divisor? What do the digits sum to each time?

**Some Examples: **

You see how fascinating and enjoying it is. In each case the difference is divisible by 9 (i.e. the common factor is 9) and the sum of the digits of the difference is always 9.

Do you think this will also work for three digit number or four-digit number. Try it out!

**5. Take 9 and add any number to it.**

**What you have observed:**

The sum of the digits of the number added to 9 is always equal to the sum of the digits of the result.** **

Take any four digit number and try the trick.** **** **

**6.** **Hand Calculator **

Your friends are amazed when you magically transform your hands into a calculator and multiply on your fingers!

Materials: Pen

Preparation

Draw these calculator keys on your palms with a ballpoint pen.

Presentation

Tell your friend that she can multiply by 9 on your hands just as she would on a regular calculator. After she enters the numbers and pushes(=) , just bend over the finger that is multiplied by 9. The fingers that are standing up tell her the answer!

**7. ****Subtraction Sorcery**

You ask a friend to work a subtraction problem on a calculator. After she tell you one digit of the answer, you are able to divulge the entire answer!

Materials

A calculator Paper and pencil** **

Finally, ask her to tell you either the first digit or the last digit of the answer. You are now able to divulge the entire answer!

How to Do It

Here are all the possible answers when you subtract two 3-digit numbers as described.

99 198 297 396 495 594 693 792 891

(__0__99)

Notice that the middle digit is always 9 and that the sum of the first digit and the last digit is 9. So just subtract what your friend tells you from 9 to get the missing digit.

An Exception

If your friend tells you that the first digit or last digit is 9, her answer will be 99.

**8.**** ****Casting out the Nines** ** **

Casting out the nines by repeatedly subtracting 9 until a remainder of less than 9 is left, or, which amounts to the same thing, dividing by 9 and noting the remainder can be done in an oddly simple way. The remainder when a number has been divided by 9 is the same as the sum of the digits (or, when that sum gives a number with two digits the sum of those digits). As the remainder not the number of nines is what you are after you can arrive at it directly. Here are two examples:

Cast the nines from 67 and find the remainder.

## FAQs

### What is the trick to the 9 multiplication? ›

Another cool trick when you multiply by nine is that we notice a pattern with the first five facts (9×1=9 to 9×5=45) to the next five facts (9×6=54 to 9×10=90). The numbers in the product are reversed. Then, if you are multiplying 9×4, you put down your fourth finger.

**What is the secret of 9 number? ›**

When any number is multiplied by nine, if the individual digits in the resulting product are added, they will always total nine as long as you keep summing the digits produced at each step until you get a one-digit number. That will always be nine.

**What is the rarest number? ›**

← 6173 6174 6175 → | |
---|---|

Senary | 44330_{6} |

Octal | 14036_{8} |

Duodecimal | 36A6_{12} |

Hexadecimal | 181E_{16} |

**Why is the number 9 so powerful? ›**

As the final numeral, the number nine holds special rank. **It is associated with forgiveness, compassion and success on the positive side as well as arrogance and self-righteousness on the negative**, according to numerologists.

**How 9 is a magic number? ›**

The number 9 is revered in Hinduism and considered a complete, perfected and divine number because **it represents the end of a cycle in the decimal system**, which originated from the Indian subcontinent as early as 3000 BC.

**What is the 9th perfect number? ›**

Rank | p | Perfect number digits |
---|---|---|

8 | 31 | 19 |

9 | 61 | 37 |

10 | 89 | 54 |

11 | 107 | 65 |

**What's the hardest 4 digit number to remember? ›**

...

What is the hardest 4 digit password?

Rank | PIN | Freq |
---|---|---|

#1 | 1234 | 10.713% |

#2 | 1111 | 6.016% |

#3 | 0000 | 1.881% |

#4 | 1212 | 1.197% |

**What's the most mysterious number? ›**

Simply put, **pi** is weird. Mathematicians call it a "transcendental number" because its value cannot be calculated by any combination of addition, subtraction, multiplication, division, and square root extraction.

**What is the weirdest number in math? ›**

The first few weird numbers are **70, 836, 4030, 5830, 7192, 7912, 9272, 10430, ...** (OEIS A006037). An infinite number of weird numbers are known to exist, and the sequence of weird numbers has positive Schnirelmann density.

**How can I memorize tables fast? ›**

**Practice skip-counting**

Skip-counting is one of the best ways for remembering multiplication tables without simply repeating the numbers. To skip-count, you start with the number you're counting by, and continue to keep adding that same number. For example, skip-counting by 2, would be, 2, 4, 6, 8, 10, etc.

### What is the trick to learn tables? ›

This is actually a very simple trick so I'll try and explain it as best I can. Use the palms of your hands. Your left hand and anything left of the finger you will put down will be the tens. Your right hand and any finger after the finger that is put down will be the ones.

**What powers does number 9 have? ›**

**Legacies**

- Telekinesis. Nine possesses Telekinesis, an ability that all Garde share.
- Legacy Transference. Nine develops this Legacy when attacked by Mogadorians at Maddy's apartment. ...
- Anti-gravity. ...
- Animal Telepathy. ...
- Super Hearing. ...
- Super Speed. ...
- Super Strength.

**What does a 9 digit number mean? ›**

According to the International place value system, a 9 digit number has **nine place values expressed as ones, tens, hundreds, thousands, ten thousands, hundred thousands, million, ten million, and the 9th place value which is hundred millions**.

**Why is 9 a lucky number? ›**

**The number nine is often associated with a divine connotation in the mystical thought and religions across the globe from ancient times**. There is both, negativity and positivity in this mysterious nine! Not to talk of the numeral 9, which is often cited as a 'lucky number' for many these days!

**What does 9 mean in numbers? ›**

In numerology, the number nine **represents completion**, as it's the last of the single-digit numbers (which are known as cardinal numbers in numerology) and the highest in value. That said, it symbolically represents a culmination of wisdom and experience, and buzzes with the energy of both endings and new beginnings.