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You are watching: Convert base 10 to base 8

In number system,

the is really important to have a an excellent knowledge of how to convert numbers native one base to one more base. Here, we will learn exactly how to convert any type of given number from base 10 to base 8.

## Decimal come Octal Conversion-

A offered number can be converted from basic 10 to any type of other basic using division method and multiplication method.

Following two situations are possible-

### Case-01: because that Numbers carrying No fountain Part-

division Method is provided to transform such numbers from basic 10 to another base. The division is performed through the compelled base.

### Steps To convert From basic 10 to basic 8-

division the given number (in base 10) with 8 till the result finally left is much less than 8. Traverse the remainders indigenous bottom to top to get the required number in basic 8.

### Case-02: because that Numbers moving A fractional Part-

To convert such numbers from base 10 to another base, real component and fractional part are cure separately.

### For genuine Part-

The steps involved in convert the real component from basic 10 to another base are same as above.

See more: How Many Hours Is 35 Miles At 65 Miles Per Hour? 35 Miles Per Hour To Miles Per Minute

### For fractional Part-

Multiplication an approach is offered to transform fractional part from basic 10 to an additional base. The multiplication is performed v the required base.

### Steps To convert From base 10 To base 8-

main point the given fraction (in base 10) v 8. Write the real part and fractional part of the an outcome so derived separately. Main point the fractional component with 8. Compose the real component and fractional component of the an outcome so obtained separately. Repeat this procedure until the fractional component remains 0. If fractional part does not terminate to 0, find the an outcome up to as many places as required.

Required Number in basic 8

= collection of real component of multiplication results derived in the over steps from optimal to bottom

Also Read- Conversion to base 10

## Problems-

Convert the adhering to numbers from base 10 to base 8-

(1032)10 (1032.6875)10 (172)10 (172.878)10

## Solution-

### 1. (1032)10

(1032)10(?)8

Using department method, we have-

From here, (1032)10 = (2010)8

### 2. (1032.6875)10

(1032.6875)10 → ( ? )8

Here, we treat the real part and fractional part separately-

### For real Part-

The real component is (1032)10 We convert the real component from basic 10 to basic 8 using division method exact same as above.

So, (1032)10 = (2010)8

### For spring Part-

The fractional part is (0.6875)10 We transform the fractional component from basic 10 to basic 8 utilizing multiplication method.

Using multiplication method, we have-

 Real part Fractional Part 0.6875 x 8 5 0.5 0.5 x 8 4 0.0

### Step-01:

main point 0.6875 through 8. Result = 5.5. Create 5 in real part and 0.5 in fountain part.

### Step-02:

multiply 0.5 through 8. Result = 4.0. Compose 4 in real part and 0.0 in spring part.

Since fractional part becomes 0, so us stop.

The fractional part terminates to 0 ~ 2 iterations. Traverse the real part column from optimal to bottom to obtain the compelled number in base 8.

From here, (0.6875)10 = (0.54)8

Combining the result of real and fractional parts, us have-

(1032.6875)10 = (2010.54)8

### 3. (172)10

(172)10 → ( ? )8

Using division method, us have-

From here, (172)10 = (254)8

### 4. (172.878)10

(172.878)10 → ( ? )8

Here, us treat the real component and fractional part separately-

### For actual Part-

The real part is (172)10 We convert the real component from base 10 to base 8 using division method very same as above.

So, (172)10 = (254)8

### For fractional Part-

The fractional part is (0.878)10 We convert the fractional part from base 10 to base 8 utilizing multiplication method.

Using multiplication method, us have-

 Real part Fractional Part 0.878 x 8 7 0.024 0.024 x 8 0 0.192 0.192 x 8 1 0.536 0.536 x 8 4 0.288

The fractional component does not terminates come 0 after numerous iterations. So, permit us uncover the value approximately 4 decimal places. Traverse the real part column from optimal to bottom to attain the required number in base 8.