1.2.2 Multiplying by 101 Trick

In the same spirit as the multiplying by 11’s trick, multiplying by 101 involves adding gap connected digits.

Example: 438 × 101

Step	Calculation	Result
Ones	1 × 8	8
Tens	1 × 3	3
Hundreds	1 × 4 + 1 × 8	12
Thousands	1 × 3 + 1	4
Ten Thousands	1 × 4	4

Answer: 44238

So you see, immediately you can write down the ones/tens digits (they are the same as what you are multiplying 101 with). Then you sum gap digits and move down the line.

Example: 8234 × 101

Step	Calculation	Result
Ones/Tens	34	34
Hundreds	2 + 4	6
Thousands	8 + 3	11
Ten Thousands	2 + 1	3
Hundred Thousands	8	8

Answer: 831634

Quick Method

For any number abcd × 101:

1. Write the last two digits as-is
2. Add digits with a gap of 2 (ones + hundreds, tens + thousands, etc.)
3. Continue moving down the line with carries

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Problem Set 1.2.2

* Questions marked with an asterisk accept answers within 5% tolerance.