Convert the numeral to a numeral in base 12. 4529 4529= =12
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Converting Decimal Numbers to Other Bases
#### Question: Convert the numeral to a numeral in base 12.
```
4529
```
#### Solution
```
4529 = [ ]₁₂
```
### Explanation:
In this exercise, you are asked to convert the decimal number 4529 to its equivalent in base 12.
#### Detailed Steps:
1. Start dividing the decimal number (4529) by 12 and keep track of the quotient and remainder.
2. The remainders, read from bottom to top, will form the base-12 number.
In this case, you perform successive divisions of 4529 by 12 until the quotient is zero. The remainder at each step represents a digit of the base 12 number starting from the least significant digit to the most significant digit (from bottom to top).
Example calculation illustration:
- **Step 1:** 4529 ÷ 12 = 377 R 5 → The remainder is 5 (least significant digit).
- **Step 2:** 377 ÷ 12 = 31 R 5 → The next digit is 5.
- **Step 3:** 31 ÷ 12 = 2 R 7 → The next digit is 7.
- **Final Step:** 2 ÷ 12 = 0 R 2 → The most significant digit is 2.
So, 4529 in base 10 is written as "2575" in base 12.
```
4529 = 2575₁₂
```](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94f92ff5-1fee-41b2-9a69-3f1799cc23e2%2Fc106bd52-1370-46ca-89ba-b2a6d0e1ca05%2Fwq038x5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Converting Decimal Numbers to Other Bases
#### Question: Convert the numeral to a numeral in base 12.
```
4529
```
#### Solution
```
4529 = [ ]₁₂
```
### Explanation:
In this exercise, you are asked to convert the decimal number 4529 to its equivalent in base 12.
#### Detailed Steps:
1. Start dividing the decimal number (4529) by 12 and keep track of the quotient and remainder.
2. The remainders, read from bottom to top, will form the base-12 number.
In this case, you perform successive divisions of 4529 by 12 until the quotient is zero. The remainder at each step represents a digit of the base 12 number starting from the least significant digit to the most significant digit (from bottom to top).
Example calculation illustration:
- **Step 1:** 4529 ÷ 12 = 377 R 5 → The remainder is 5 (least significant digit).
- **Step 2:** 377 ÷ 12 = 31 R 5 → The next digit is 5.
- **Step 3:** 31 ÷ 12 = 2 R 7 → The next digit is 7.
- **Final Step:** 2 ÷ 12 = 0 R 2 → The most significant digit is 2.
So, 4529 in base 10 is written as "2575" in base 12.
```
4529 = 2575₁₂
```
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