# How to Convert an Octal Number Into Decimal | Octal to Decimal Conversion

Hello guys, In our todayโs blog, we will see that how can we convert the Octal number Into a decimal number system. Before we starting our blog Letโs take a little recap about Octal and Decimal numbers so that you can revise this topic.

Octal Number: Octal numbers is a numbers that it uses the digit 0 to 8(0,1,2,3,4,5,6,7). Which means their base is 8. So, it is called โOctal Numberโ.

Examples of Octal Numbersโ 68, 108, 278, 348, 1258 etc.

Decimal Number: Octal number is a numbers that uses the digit o to 9(0,1,2,3,4,5,6,7,8,9). Which means their base is 10. So, it is called โDecimal numberโ

Examples of Decimal Numbers: 110, 810, 1610, 2710, 15610, etc.

For better understanding let start directly with the exampleโฆ

To convert this number, we have to multiply every place of digit of an octal number with 8 to the power of their corresponding values.

Example: If an octal number has a one-digit number e.g. 58, it means it is multiplied by 80 like this 5 x 80 = 510 because it has only a one-digit number. What, If the octal number has three-digit number like 4528 then it will multiplied by 82,81,80 like this 4 x 82 + 5 x 81 + 2 x 80 = 29810.

Thatโs itโฆ

Also, go for this article to know how to multiply every place of digit with their corresponding Position/Values: Binary to decimal Conversion.

Example 1: Convert the Octal Number (7)8 into Decimal?

Sol:

```=(7)8

= 7x80

= 7x1

= 7

Hence, the decimal number is (7)10
```

Example 2: Convert an Octal Number (14)8 into Decimal?

Sol:

```=(14)8

= 1x81 + 4x80

= 1x8 + 4x1

= 12

Hence, the decimal number is (12)10
```

Example 3: Convert an Octal Number (63)8 into Decimal?

Sol:

```=(63)8

= 6x81 + 3x80

= 6x8 + 3x1

= 48 + 3

= 51

Hence, the decimal number is (51)10
```

Example 4: Convert an Octal Number (275)8 into Decimal?

Sol:

```=(275)8

= 2x82 + 7x81 + 5x80

= 2x64 + 7x8 + 5x1

= 128 + 56 + 5

= 189

Hence, the decimal number is (186)10
```

Example 5: Convert an Octal number (756)8 into Decimal?

Sol:

```=(756)8

= 7x82 + 5x81 + 6x80

= 7x64 + 5x8 + 6x1

= 448 + 40 + 6

= 494

Hence, the decimal number is (186)10
```

Example 6: Convert an Octal Number (1025)8 into Decimal?

Sol:

```=(1025)8

= 1x83 + 0x82 + 2x81 + 5x80

= 1x512 + 0x64 + 2x8 + 5x1

= 512 + 0 + 16 + 5

= 533

Hence, the decimal number is (533)10
```

Example 7: Convert an Octal Number (6725)8 into Decimal?

Sol:

```=(6725)8

= 6x83 + 7x82 + 2x81 + 5x80

= 6 x 512 + 7 x 64 + 2 x 8 + 5 x 1

= 3072 + 448 + 16 + 5

= 3541

Hence, the decimal number is (3541)10
```

Now, we are going to solve some decimal point questions and letโs see how they solveโฆ

Example 8: Convert an Octal Number (2.4)8 into Decimal?

Sol:

```=(2.4)8

= 2x80 + 4x8-1

= 2 + 4/8

= (16+4)/8

= 20/8

Hence, the decimal number is (2.5)10
```

Example 9: Convert an Octal Number (4.32)8 into Decimal?

Sol:

```=(4.32)8

= 4x80 + 3x8-1 + 2x8-2

= 4 x 1 + 3 x 1/8 + 2 x 1/82

= 4 + 3/8 + 2/64

= 4 + 3/8 + 2/32

= (128+12+1)/32

= 141/32

= 4.40625

Hence, the decimal number is (4.40625)10
```

Example 10: Convert an Octal Number (52.1)8 into Decimal?

Sol:

```=(52.1)8

= 5x81 + 2x80 + 1x8-1

= 40 + 2 + 1/8

= (320+16+1)/8

= 337/8

= 42.125

Hence, the decimal number is (42.125)10
```

Example 11: Convert an Octal Number (456.34)8 into Decimal?

Sol:

```=(456.34)8

= 4x82 + 5x81 + 6x80 + 3x8-1 + 4x8-2

= 256 + 40 + 6 + 3/8 + 1/16

= (4096+640+96+6+1)/16

= 302.4375

Hence, the decimal number is (302.4375)10
```

Example 12: Convert an Octal Number (12.634)8 into Decimal?

Sol:

```=(12.634)8

= 1x81 + 2x80 + 6x8-1 + 3x8-2 + 4x8-3

= 1x8 + 2x1 + 6x1/8 + 3x1/64 + 4x1/512

=  8 + 2 + 6/8 + 3/64 + 1/128

= (1024+256+96+6+1)/128

= 10.8046875

Hence, the decimal number is (10.8046875)10
```

## Conclusion:

I have told you about how to convert the octal number into the Decimal Number. If you have any questions then tell me in the comment section.

So, thatโs for todayโs blog guys. We will meet again with the new topic, till then you read our old blog and tell me if I have made any mistake in my content so please tell me in the comment section so that I will fix it as soon as possible. And, also give us your feedback about this website.