Answer :
To solve this problem and convert the given Babylonian numeral to a Hindu-Arabic numeral, let's break down and interpret each part of the Babylonian numeral step by step. Here's how we can do it:
### Step 1: Identify and separate the symbols
The given Babylonian numeral is:
[tex]\[ \vee \vee << \vee \vee \][/tex]
We'll separate this numeral into its individual symbols based on their values.
### Step 2: Assign values to each symbol
Using the given table:
- The symbol [tex]\(\vee\)[/tex] corresponds to the number 1.
- The symbol [tex]\(<\)[/tex] corresponds to the number 10.
### Step 3: Count the occurrences of each symbol
In the numeral [tex]\(\vee \vee << \vee \vee\)[/tex], we see:
- Two [tex]\(\vee\)[/tex] symbols at the beginning.
- Two [tex]\(<\)[/tex] symbols in the middle.
- Two [tex]\(\vee\)[/tex] symbols at the end.
### Step 4: Calculate the total value
Now, convert each part to its Hindu-Arabic equivalent:
- There are 2 [tex]\(\vee\)[/tex] symbols at the beginning. Each [tex]\(\vee\)[/tex] represents 1, so this part totals: [tex]\(2 \times 1 = 2\)[/tex].
- There are 2 [tex]\(<\)[/tex] symbols in the middle. Each [tex]\(<\)[/tex] represents 10, so this part totals: [tex]\(2 \times 10 = 20\)[/tex].
- There are 2 [tex]\(\vee\)[/tex] symbols at the end. Each [tex]\(\vee\)[/tex] represents 1, so this part totals: [tex]\(2 \times 1 = 2\)[/tex].
### Step 5: Sum the values
Add the three parts together to find the total value:
[tex]\[ 2 (\text{from the first two } \vee) + 20 (\text{from the two } <) + 2 (\text{from the last two } \vee) = 24 \][/tex]
### Conclusion
The given Babylonian numeral [tex]\(\vee \vee << \vee \vee\)[/tex] converts to the Hindu-Arabic numeral 24.
Thus, the answer is:
[tex]\[ \boxed{24} \][/tex]
### Step 1: Identify and separate the symbols
The given Babylonian numeral is:
[tex]\[ \vee \vee << \vee \vee \][/tex]
We'll separate this numeral into its individual symbols based on their values.
### Step 2: Assign values to each symbol
Using the given table:
- The symbol [tex]\(\vee\)[/tex] corresponds to the number 1.
- The symbol [tex]\(<\)[/tex] corresponds to the number 10.
### Step 3: Count the occurrences of each symbol
In the numeral [tex]\(\vee \vee << \vee \vee\)[/tex], we see:
- Two [tex]\(\vee\)[/tex] symbols at the beginning.
- Two [tex]\(<\)[/tex] symbols in the middle.
- Two [tex]\(\vee\)[/tex] symbols at the end.
### Step 4: Calculate the total value
Now, convert each part to its Hindu-Arabic equivalent:
- There are 2 [tex]\(\vee\)[/tex] symbols at the beginning. Each [tex]\(\vee\)[/tex] represents 1, so this part totals: [tex]\(2 \times 1 = 2\)[/tex].
- There are 2 [tex]\(<\)[/tex] symbols in the middle. Each [tex]\(<\)[/tex] represents 10, so this part totals: [tex]\(2 \times 10 = 20\)[/tex].
- There are 2 [tex]\(\vee\)[/tex] symbols at the end. Each [tex]\(\vee\)[/tex] represents 1, so this part totals: [tex]\(2 \times 1 = 2\)[/tex].
### Step 5: Sum the values
Add the three parts together to find the total value:
[tex]\[ 2 (\text{from the first two } \vee) + 20 (\text{from the two } <) + 2 (\text{from the last two } \vee) = 24 \][/tex]
### Conclusion
The given Babylonian numeral [tex]\(\vee \vee << \vee \vee\)[/tex] converts to the Hindu-Arabic numeral 24.
Thus, the answer is:
[tex]\[ \boxed{24} \][/tex]
