Convert the following: (11.2)10 = (?)8

To convert a decimal number to an octal number, you need to follow these steps:

1. Divide the decimal number by 8.
2. Write down the remainder.
3. Divide the quotient of the previous division by 8.
4. Repeat steps 2 and 3 until the quotient is 0.
5. The octal number is the remainders, written in reverse order (from bottom to top).

Let's convert (11.2)10 to octal:

Step 1: Convert the integer part

First, we convert the integer part, which is 11.

Division by 8	Quotient	Remainder
11 ÷ 8	1	3
1 ÷ 8	0	1

Reading the remainders from bottom to top, we get (13)8.

Step 2: Convert the fractional part

Next, we convert the fractional part, which is 0.2.

To convert the fractional part, we need to follow these steps:

1. Multiply the fraction by 8.
2. Write down the whole number part.
3. Multiply the fractional part of the result from step 1 by 8.
4. Repeat steps 2 and 3 until the fraction part is zero or until you have a sufficient number of digits after the decimal point.

Multiplication by 8	Whole Number	Fraction
0.2 * 8	1	0.6
0.6 * 8	4	0.8
0.8 * 8	6	0.4
0.4 * 8	3	0.2

We can stop here as we have a sufficient number of digits after the decimal point. Reading the whole numbers from top to bottom, we get (0.1463)8.

So, (11.2)10 = (13.1463)8.