How to multiply any number by 101?

In this tutorial, we are going see an interesting class of numbers like 101, 203, 10001, 201 etc. Notice an important thing here. You have 2 different numbers (may be same or different) at the end and you have 1 or more zeros in between.

What is so special, you might think. It turns out, that when you multiply any number (multiplicand) with numbers like 101, 1001, you just repeat the multiplicand twice.

Let us understand the shortcut with a very simple example: Let’s say we need to multiply 23 x 101.

multiplying_by_101

 

When you multiply any 2-digit number with 101, you just repeat 23 twice.

Similarly, 39 x 101 would be :

multiplying_by_101_2

Very easy right 🙂

On the similar lines, can you mentally calculate?

  • 12 x 101
  • 13 x 101
  • 89 x 101
  • 99 x 101

 

Multiplication of a 3-digit number with 101

 

Suppose, we have to multiply a 3-digit number with 101, the steps are slightly different from the previous case. Let us consider an example so that it is clear.

Let’s say we want to multiply 243 x 101

multiplying_by_101_3

 

Step 1 :  The first 2 –digits  24 will become the first part of the answer.

Step 2 :  The last 2 –digits  43 will become the last part of the answer.

Step 3 :  The middle digit in the answer is obtained by adding the first and the last digit of the multiplicand.

So, the only difference is instead of repeating the whole digit, you repeat the first 2 and the last 2 digits.

 

Can you multiply 856 x 101 ?

multiplying_by_101_4

 

Notice the carry-over in the addition. We can retain only 1-digit in the addition.

 

It does not always have to be 101. The steps remain same even if the number is say 203, 304. However, in this case, the answer will be scaled according to the multiplicand.

Let’s say we need to multiply 43 x 205. The steps are illustrated in the figure.

 

multiplying_by_101_5

 

Instead of 101, we have 205 here. So, you scale the first part of the answer by 2 and last part by 5.

Step 1 : The multiplicand 43 is doubled to get 86 to get the first part of the answer.

Step 2 : The multiplicand 43 is multiplied by 5 to get 215. However, we can retain only 2-digits. So, 2 is carry-forward to get the final answer as 8815.

Similarly,  can you try 74 x 603 ?

 

multiplying_by_101_6

 

Multiplication by 1001

 

If the multiplier is 1001, you just repeat the 3-digits of the multiplicand twice. Let’s say we want to multiply 359 x 1001.

 

multiplying_by_101_7

 So, 359 x 101 = 359359

Similarly, 453 x 1001 = 453453

 

Now consider the multiplication, 435 x 3002

multiplying_by_101_8

 

Step 1 : The multiplicand 435 is multiplied by 3 to get 1305 which becomes the first part of the answer.

Step 2 : The multiplicand 435 is multiplied by 2 to get 870 which forms the RHS part of the answer.

 

Now, what if the multiplicand is a 2-digit number.  Notice the multiplication 43 x 3002.

 

multiplying_by_101_9

 

A zero is added in the beginning so that the number of digits in multiplicand is 1 less than the multiplier. The rest of the steps remains same.

On the similar lines, can you multiply :

  • 23 x 1001
  • 848 x 1001
  • 72 x 2004
  • 834 x 2002

 

Important:

  • Even if one of number is bigger say 10001, 1000001, the multiplicand is repeated twice to get the final answer.
  • Similarly if you multiply the number 24 by 10101, you notice that the multiplicand is repeated thrice and  4 times if the multiplicand is 1010101 and so on.

I hope you find this tutorial useful. Please leave a comment if certain point in the tutorial is not clear.

Kiran Chandrashekhar

Hey, Thanks for dropping by. My name is Kiran Chandrashekhar. I am a full-time software freelancer. I love Maths and Mathematical Shortcuts. Numbers fascinate me. I will be posting articles on Mathematical Shortcuts, Software Tips, Programming Tips in this website. I love teaching students preparing for various competitive examinations. Read my complete story.

6 Comments

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