# Digit Cloning With Multiplication!

## Surely, you know what happens when you multiply single-digit numbers by 11, right?

Mr. Eleven Primen, Distant Member of the Digit Family

## If you multiply 2-digit numbers by 101, you get a similar effect in the product! Observe the examples below:

12 × 101 = 1,212

25 × 101 = 2,525

36 × 101 = 3,636

47 × 101 = 4,747

59 × 101 = 5,959

## If you multiply 3-digit numbers by 1,001...

123 × 1,001 = 123,123

279 × 1,001 = 279,279

380 × 1,001 = 380,380

456 × 1,001 = 456,456

517 × 1,001 = 517,517

## If you multiply 4-digit numbers by 10,001...

1,849 × 10,001 = 18,491,849

2,084 × 10,001 = 20,842,084

3692 × 10,001 = 36,923,692

## For 5-digit numbers, multiply by 100,001.

## For 6-digit numbers, multiply by 1,000,001.

## For 7-digit numbers, multiply by 10,000,001.

The more digits the *multiplicand* has, the more **zeroes** you must put in the "number sandwich". (Consider the **1's** the bread slices) The number sandwich, as I called it, is the* multiplier.* By multiplying correctly, you get these special products which make it look like you cloned all the digits in the multiplicand! But how many **zeroes** should you put between the **1's**? Simple! **[The number of digits the multiplicand has]** - **1** = **[The number of zeroes you should put in the multiplying number sandwich!]**

__Here's the formula again below with variables:__

x - 1 = y

x = The number of digits the multiplicand has

y = The number of zeroes you should put in the multiplying number sandwich!

__But also, consider this function:__

10^{x} + 1 = y

The variable *y* IS the number sandwich in this function. All of the number sandwiches above are equal to **1 + a power of 10.**

If you multiply by the correct number sandwich, you'll clone all of the multiplicand's digits, which you'll get in the product! The digits are cloned just like how Pixelman & Lady Fingersandtoes cloned themselves by drinking Multi-Milk in the cartoon above!

But beware, because if the number sandwich doesn't have enough zeroes, something like this will happen:

If it has too many zeroes, something like this will happen:

144 × 100,001 = 14,400,144

## But guess what...You can use double-decker number sandwiches, triple-deckers, quadruple-deckers, et cetera, which makes this math trick even cooler!

54 × 10,101 = 545,454

216 × 1,001,001,001 = 216,216,216,216

78 × 101,010,101 = 7,878,787,878

## But put the exact same amount of zeroes between the 1's! (The 1's are the bread slices of the number sandwiches!) Finally, use 1's & zeroes only; don't use any of the other 8 digits in the number sandwiches or this math trick just won't work!

Something like this will happen:

#### Note: I like to put commas in large numbers because it helps you count how many digits they have. A comma is put after every 3 digit columns.

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© Derek Cumberbatch