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Unit Digit Tricks and Tips

1. Unit Digit of a Product

To find the unit digit of a product, multiply the last digits of each number.

Example: Find the unit digit of (121 × 76 × 528 × 172).

Multiply the last digits: (1 × 6 × 8 × 2 = 96).

The unit digit of 96 is 6.

MCQs on Unit Digit of a Product

  1. What is the unit digit of (123 × 456 × 789)?
    1. 2
    2. 4
    3. 6
    4. 8
    Answer: B) 4
  2. What is the unit digit of (321 × 654 × 987)?
    1. 2
    2. 4
    3. 6
    4. 8
    Answer: D) 8

2. Unit Digit of Powers

To find the unit digit of a number raised to a power, use the cyclicity of the number.

Cyclicity Table:

2: 2, 4, 8, 6
3: 3, 9, 7, 1
4: 4, 6
5: 5
6: 6
7: 7, 9, 3, 1
8: 8, 4, 2, 6
9: 9, 1

Example: Find the unit digit of (249).

Divide the exponent by 4: (49 ÷ 4 = 12) with a remainder of 1.

So, (249) has the same unit digit as (21), which is 2.

MCQs on Unit Digit of Powers

  1. What is the unit digit of (315)?
    1. 1
    2. 3
    3. 7
    4. 9
    Answer: C) 7
  2. What is the unit digit of (722)?
    1. 1
    2. 3
    3. 7
    4. 9
    Answer: D) 9

3. Special Cases

For numbers ending in 0, 1, 5, or 6, the unit digit remains the same regardless of the power.

Example: ((235)27) has a unit digit of 5.

((126)344) has a unit digit of 6.

MCQs on Special Cases

  1. What is the unit digit of (5100)?
    1. 0
    2. 1
    3. 5
    4. 6
    Answer: C) 5
  2. What is the unit digit of (650)?
    1. 0
    2. 1
    3. 5
    4. 6
    Answer: D) 6

4. General Rule for Other Numbers

For numbers ending in 2, 3, 4, 7, 8, or 9:

  1. Divide the exponent by 4.
  2. Use the remainder as the power of the last digit.
  3. If the remainder is 0, use 4 as the power.

Example 1: ((327)22)

Divide 22 by 4: Remainder is 2.

Last digit is 7: (72 = 49).

Unit digit is 9.

Example 2: ((28)36)

Divide 36 by 4: Remainder is 0 (use 4).

Last digit is 8: (84 = 4096).

Unit digit is 6.

MCQs on General Rule for Other Numbers

  1. What is the unit digit of (413)?
    1. 2
    2. 4
    3. 6
    4. 8
    Answer: B) 4
  2. What is the unit digit of (925)?
    1. 1
    2. 3
    3. 7
    4. 9
    Answer: D) 9

Tips and Tricks

Tip 1: Memorize the cyclicity of numbers to quickly determine the unit digit.

Tip 2: For large exponents, always divide by 4 and use the remainder to simplify the problem.

Tip 3: Practice with different numbers to get comfortable with the patterns.

Important Points

1. The unit digit of a product depends only on the unit digits of the numbers involved.

2. The cyclicity of numbers helps in determining the unit digit of powers.

3. Special cases (0, 1, 5, 6) always retain their unit digit regardless of the power.