Try to answer the following:

What is the units digit (last digit) of 22011 ?

THE MAGIC REMAINDER TECHNIQUE

(For numbers with a very large exponents)

To get the last digit of a number with a very large exponent:

Step 1. Get last 2 digits of the exponent.

Step 2. Divide by 4 and get remainder.

Step 3. The remainder becomes the new exponent.

Example:

What is the units digit (last digit) of 22011 ?

Step 1. 22011 –> 211

Step 2. Divide 11 by 4. Remainder = 3

Step 3. 211 –> 23 = 8

Answer: Last digit = 8

Exception to the Rule: If the remainder is zero, exponent should be 4, not 0.

Example: 312 –> 34 = 81. Last digit = 1.

NOW, IT’S YOUR TURN!

What is the units digit of 32014 ? What is the units digit of 7326 ? What is the units digit of 9878 ? What is the units digit of 62015 ? CHALLENGE: What is the units digit of 1232014 ?

Reflection for the Pro (if you are BRAVE enough!)

If the base has more than one digit, what shortcut can you suggest? Think of a faster way if the base is 4 or 9. What if the base is 1, 5, 6 or 0?

–Wacks Formula 🙂

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ShortCut #2: The Wacks Middle Finger Technique

Disclaimer: The name of the formula is purely for fun, and does not discredit others who might have discovered the same formula independently.