# Find Unit digit

__Unit digit__

The unit digit of any number is called that which is on the one's place of the number, in other words, the first place from the right e.g.- the unit digit of 28 is 8, the unit digit of 279 is 9, the unit digit of 24560 is 0 and so on.

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There are total 10 digit in maths 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 divide them into three parts (2, 3, 7, 8), (5, 6, 0, 1 ) and (4, 9)

### How to find the unit digit of 2, 3, 7, 8?

If the unit's place of a number is 2, 3, 7, 8 and it is in power, then to get
the unit digit, divide the power by 4, the remainder is written in the power
if **the remainder is 0, so put 4 in the power.** Let us understand this
with some questions.

**e.g.-**

**Qus**. What is the unit digit of 2^{43} ?

**Solution**-

= 2^{43}

= 2^{43/4} [43/4 Remainder = 3]

= 2^{3}

= 8

So, the number of unit digit is 8.

**Qus**. What is the unit digit of 7^{49 }?

**Solution**-

= 7^{49/4}

= 7^{1} [49/4 Remainder = 1]

= 7

So, the number of unit digit is 7.

**Qus**. What is the unit digit of 8^{400 }?

**Solution**-

= 8^{400/4}

= 8^{0} [400/4 Remainder = 0]

= 8^{4} [**The remainder is 0, so put 4 in the power.]**

**= **409__6__

So, the number of unit digit is 6.

**Qus**. What is the unit digit of 333^{888} +
888^{222} ?

**Solution**-

= 333^{888} + 888^{222}

= 3^{888/4} + 8^{222/4} [Solve by taking unit
digit only]

= 3^{0} + 8^{2} [888/4
Remainder = 0, 222/4 Remainder = 2]

= 3^{4} + 64 [**The remainder is 0, so put 4 in the power.]**

= 81 +64

= 14__5__

So, the number of unit digit is 5.

### How to find the unit digit of 5, 6, 0, 1?

Whatever is the power of all these numbers(5, 6, 0, 1), their unit digit is the same number.

**e.g.-**

**Qus**. What is the unit digit of 5^{3 }?

**Solution**-

= 5^{3}

= 12__5__

So, the number of unit digit is 5.

**Qus**. What is the unit digit of 5^{9} ?

**Solution**-

= 5^{9}

= 195312__5__

So, the number of unit digit is 5.

**Qus**. What is the unit digit of 0^{400} ?

**Solution**-

= 0^{400}

**= **0

So, the number of unit digit is 0.

**Qus**. What is the unit digit of 6^{8} ?

**Solution**-

= 6^{8}

=167961__6__

So, the number of unit digit is 6.

It is clear from all the above questions that no matter what is the power of 5, 6, 0, 1, the unit digit will get the same number.

### How to find the unit digit of 4, 9?

If the unit's place of a number is 4, 9 and it is in the power, then to get the unit's digit, first, it has to be noticed whether the power is even or odd. If the power of 4 is odd, then the unit digit will be 4 but If the power is even, the unit digit will be 6. Similarly, if the power of 9 is odd then the unit digit will be 9 but if the power is even then the unit digit will be 1.

**e.g.-**

**Qus**. What is the unit digit of 4^{7} ?

**Solution**-

= 4^{7} [Odd Power]

= 1638__4__

So, the number of unit digit is 4.

**Qus**. What is the unit digit of 4^{12} ?

**Solution**-

= 4^{12} [Even Power]

= 195312__5__

So, the number of unit digit is 5.

**Qus**. What is the unit digit of 9^{9} ?

**Solution**-

= 9^{9}
[Odd Power]

=38742048__9__

So, the number of unit digit is 9.

**Qus**. What is the unit digit of 9^{8 }?

**Solution**-

= 9^{8} [Even Power]

= 4304672__1__

So, the number of unit digit is 1.

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