Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
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 our answers were helpful. Return anytime for more information and answers to any other questions you may have. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
