https://file.aiquickdraw.com/mathbot/file/1729121180332safmt55y.jpg

The problem in the image asks you to convert the base-five number \( 1120_5 \) into its base-ten (decimal) equivalent.

To convert from base-five to base-ten, we follow this process:

1. Write the base-five number in expanded form, using powers of 5.
   
   \[
   1120_5 = 1 \times 5^3 + 1 \times 5^2 + 2 \times 5^1 + 0 \times 5^0
   \]

2. Calculate each power of 5:
   
   \[
   5^3 = 125, \quad 5^2 = 25, \quad 5^1 = 5, \quad 5^0 = 1
   \]

3. Multiply each digit by its corresponding power of 5:

   \[
   1 \times 125 = 125
   \]
   \[
   1 \times 25 = 25
   \]
   \[
   2 \times 5 = 10
   \]
   \[
   0 \times 1 = 0
   \]

4. Add the results together:

   \[
   125 + 25 + 10 + 0 = 160
   \]

So, \( 1120_5 \) in base-ten is \( 160_{10} \).

Would you like more details or have any further questions?

Here are some related questions to expand your understanding:

1. How do you convert a base-ten number to a base-five number?
2. What is the base-five equivalent of \( 200_{10} \)?
3. How does the conversion process change for other bases, like base-eight or base-twelve?
4. What are some common uses of non-decimal bases in computing or mathematics?
5. How can you verify your answer when converting from one base to another?

**Tip:** Always double-check by expanding the base number into powers of its base, then calculate step-by-step to avoid errors.

The following number is a base-five numeral. Convert this to a base-ten numeral: 1120_5 = ?_10

Learn how to convert the base-five numeral 1120_5 to a base-ten number using step-by-step base conversion techniques. Suitable for Grades 7-9, this problem explains the use of powers of 5 and provides a detailed solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation