Westonci.ca is the premier destination for reliable answers to your questions, brought to you by a community of experts. Explore in-depth answers to your questions from a knowledgeable community of experts across different fields. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
Sagot :
Sure, let's convert each of these base-six numbers to base-ten numbers step by step.
### 1. Converting [tex]\(555_{\text{six}}\)[/tex] to base ten:
The notation [tex]\(555_{\text{six}}\)[/tex] means that each digit represents a power of six.
[tex]\[ 555_{\text{six}} = 5 \cdot 6^2 + 5 \cdot 6^1 + 5 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 5 \cdot 6^2 = 5 \cdot 36 = 180 \][/tex]
[tex]\[ 5 \cdot 6^1 = 5 \cdot 6 = 30 \][/tex]
[tex]\[ 5 \cdot 6^0 = 5 \cdot 1 = 5 \][/tex]
Adding these together:
[tex]\[ 180 + 30 + 5 = 215 \][/tex]
So, [tex]\(555_{\text{six}} = 215_{\text{ten}}\)[/tex].
### 2. Converting [tex]\(215_{\text{six}}\)[/tex] to base ten:
[tex]\[ 215_{\text{six}} = 2 \cdot 6^2 + 1 \cdot 6^1 + 5 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 2 \cdot 6^2 = 2 \cdot 36 = 72 \][/tex]
[tex]\[ 1 \cdot 6^1 = 1 \cdot 6 = 6 \][/tex]
[tex]\[ 5 \cdot 6^0 = 5 \cdot 1 = 5 \][/tex]
Adding these together:
[tex]\[ 72 + 6 + 5 = 83 \][/tex]
So, [tex]\(215_{\text{six}} = 83_{\text{ten}}\)[/tex].
### 3. Converting [tex]\(110_{\text{six}}\)[/tex] to base ten:
[tex]\[ 110_{\text{six}} = 1 \cdot 6^2 + 1 \cdot 6^1 + 0 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 1 \cdot 6^2 = 1 \cdot 36 = 36 \][/tex]
[tex]\[ 1 \cdot 6^1 = 1 \cdot 6 = 6 \][/tex]
[tex]\[ 0 \cdot 6^0 = 0 \cdot 1 = 0 \][/tex]
Adding these together:
[tex]\[ 36 + 6 + 0 = 42 \][/tex]
So, [tex]\(110_{\text{six}} = 42_{\text{ten}}\)[/tex].
### 4. Converting [tex]\(1000_{\text{six}}\)[/tex] to base ten:
[tex]\[ 1000_{\text{six}} = 1 \cdot 6^3 + 0 \cdot 6^2 + 0 \cdot 6^1 + 0 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 1 \cdot 6^3 = 1 \cdot 216 = 216 \][/tex]
[tex]\[ 0 \cdot 6^2 = 0 \cdot 36 = 0 \][/tex]
[tex]\[ 0 \cdot 6^1 = 0 \cdot 6 = 0 \][/tex]
[tex]\[ 0 \cdot 6^0 = 0 \cdot 1 = 0 \][/tex]
Adding these together:
[tex]\[ 216 + 0 + 0 + 0 = 216 \][/tex]
So, [tex]\(1000_{\text{six}} = 216_{\text{ten}}\)[/tex].
### 5. Converting [tex]\(82_{\text{six}}\)[/tex] to base ten:
[tex]\[ 82_{\text{six}} = 8 \cdot 6^1 + 2 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 8 \cdot 6^1 = 8 \cdot 6 = 48 \][/tex]
[tex]\[ 2 \cdot 6^0 = 2 \cdot 1 = 2 \][/tex]
Adding these together:
[tex]\[ 48 + 2 = 50 \][/tex]
So, [tex]\(82_{\text{six}} = 50_{\text{ten}}\)[/tex].
### Summary:
[tex]\[ \begin{align*} 555_{\text{six}} & = 215_{\text{ten}} \\ 215_{\text{six}} & = 83_{\text{ten}} \\ 110_{\text{six}} & = 42_{\text{ten}} \\ 1000_{\text{six}} & = 216_{\text{ten}} \\ 82_{\text{six}} & = 50_{\text{ten}} \end{align*} \][/tex]
### 1. Converting [tex]\(555_{\text{six}}\)[/tex] to base ten:
The notation [tex]\(555_{\text{six}}\)[/tex] means that each digit represents a power of six.
[tex]\[ 555_{\text{six}} = 5 \cdot 6^2 + 5 \cdot 6^1 + 5 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 5 \cdot 6^2 = 5 \cdot 36 = 180 \][/tex]
[tex]\[ 5 \cdot 6^1 = 5 \cdot 6 = 30 \][/tex]
[tex]\[ 5 \cdot 6^0 = 5 \cdot 1 = 5 \][/tex]
Adding these together:
[tex]\[ 180 + 30 + 5 = 215 \][/tex]
So, [tex]\(555_{\text{six}} = 215_{\text{ten}}\)[/tex].
### 2. Converting [tex]\(215_{\text{six}}\)[/tex] to base ten:
[tex]\[ 215_{\text{six}} = 2 \cdot 6^2 + 1 \cdot 6^1 + 5 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 2 \cdot 6^2 = 2 \cdot 36 = 72 \][/tex]
[tex]\[ 1 \cdot 6^1 = 1 \cdot 6 = 6 \][/tex]
[tex]\[ 5 \cdot 6^0 = 5 \cdot 1 = 5 \][/tex]
Adding these together:
[tex]\[ 72 + 6 + 5 = 83 \][/tex]
So, [tex]\(215_{\text{six}} = 83_{\text{ten}}\)[/tex].
### 3. Converting [tex]\(110_{\text{six}}\)[/tex] to base ten:
[tex]\[ 110_{\text{six}} = 1 \cdot 6^2 + 1 \cdot 6^1 + 0 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 1 \cdot 6^2 = 1 \cdot 36 = 36 \][/tex]
[tex]\[ 1 \cdot 6^1 = 1 \cdot 6 = 6 \][/tex]
[tex]\[ 0 \cdot 6^0 = 0 \cdot 1 = 0 \][/tex]
Adding these together:
[tex]\[ 36 + 6 + 0 = 42 \][/tex]
So, [tex]\(110_{\text{six}} = 42_{\text{ten}}\)[/tex].
### 4. Converting [tex]\(1000_{\text{six}}\)[/tex] to base ten:
[tex]\[ 1000_{\text{six}} = 1 \cdot 6^3 + 0 \cdot 6^2 + 0 \cdot 6^1 + 0 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 1 \cdot 6^3 = 1 \cdot 216 = 216 \][/tex]
[tex]\[ 0 \cdot 6^2 = 0 \cdot 36 = 0 \][/tex]
[tex]\[ 0 \cdot 6^1 = 0 \cdot 6 = 0 \][/tex]
[tex]\[ 0 \cdot 6^0 = 0 \cdot 1 = 0 \][/tex]
Adding these together:
[tex]\[ 216 + 0 + 0 + 0 = 216 \][/tex]
So, [tex]\(1000_{\text{six}} = 216_{\text{ten}}\)[/tex].
### 5. Converting [tex]\(82_{\text{six}}\)[/tex] to base ten:
[tex]\[ 82_{\text{six}} = 8 \cdot 6^1 + 2 \cdot 6^0 \][/tex]
Breaking it down:
[tex]\[ 8 \cdot 6^1 = 8 \cdot 6 = 48 \][/tex]
[tex]\[ 2 \cdot 6^0 = 2 \cdot 1 = 2 \][/tex]
Adding these together:
[tex]\[ 48 + 2 = 50 \][/tex]
So, [tex]\(82_{\text{six}} = 50_{\text{ten}}\)[/tex].
### Summary:
[tex]\[ \begin{align*} 555_{\text{six}} & = 215_{\text{ten}} \\ 215_{\text{six}} & = 83_{\text{ten}} \\ 110_{\text{six}} & = 42_{\text{ten}} \\ 1000_{\text{six}} & = 216_{\text{ten}} \\ 82_{\text{six}} & = 50_{\text{ten}} \end{align*} \][/tex]
We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.
