To convert a number from base 8 (octal) to base 10 (decimal), follow these steps:

### Step 1: Understand the number in base 8.
The number is \(20.45_8\), which means:
\[
20.45_8 = 2 \times 8^1 + 0 \times 8^0 + 4 \times 8^{-1} + 5 \times 8^{-2}
\]

### Step 2: Calculate the integer part.
\[
2 \times 8^1 = 2 \times 8 = 16
\]
\[
0 \times 8^0 = 0
\]
So, the integer part is \(16\).

### Step 3: Calculate the fractional part.
\[
4 \times 8^{-1} = 4 \times \frac{1}{8} = 4 \times 0.125 = 0.5
\]
\[
5 \times 8^{-2} = 5 \times \frac{1}{64} = 5 \times 0.015625 = 0.078125
\]
So, the fractional part is \(0.5 + 0.078125 = 0.578125\).

### Step 4: Add the integer and fractional parts.
\[
16 + 0.578125 = 16.578125
\]

Thus, \(20.45_8\) in base 10 is **16.578125**.

Would you like more details on any step or have any further questions?

Here are 5 related questions you might find interesting:
1. How do you convert a number from base 10 to base 8?
2. What is the base 10 value of 34.25 in base 8?
3. Can you explain how to convert a base 2 number to base 10?
4. What is the importance of fractional parts in non-decimal bases?
5. How would you handle repeating decimals in base conversions?

**Tip:** When converting from any base to base 10, remember to treat digits after the decimal point as negative powers of the base.

Learn how to convert 20.45 from base 8 (octal) to base 10 with this comprehensive guide. The solution breaks down the conversion process into integer and fractional parts using key formulas. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation