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Convert Given Mayan Numeral to Equivalent Base-10 Number
Mathematics
Grade 7 (Junior High School)
Question Content
Given the following Mayan Number, write the equivalent Base-10 number in the Answer Box. Each row (place value) is separated with white space. Note: There are FOUR place values in the number below: [Top row: 3 dots; Second row: 1 bar (5) + 3 dots = 8; Third row: 1 dot over a bar (5) = 6; Bottom row: 2 dots over a bar (5) = 7]
Correct Answer
3079
Detailed Solution Steps
1
Step 1: Recall that Mayan numerals use a base-20 (vigesimal) place value system, where each row represents a power of 20, starting from the bottom row as 20^0, then moving up to 20^1, 20^2, 20^3.
2
Step 2: Translate each Mayan row to its base-10 value: Bottom row (20^0 place): 1 bar (5) + 2 dots = 5 + 2 = 7; Third row (20^1 place): 1 bar (5) + 1 dot = 5 + 1 = 6; Second row (20^2 place): 1 bar (5) + 3 dots = 5 + 3 = 8; Top row (20^3 place): 3 dots = 3.
3
Step 3: Calculate the value of each place by multiplying the row's value by its corresponding power of 20: Top row: 3 × 20^3 = 3 × 8000 = 2400; Second row: 8 × 20^2 = 8 × 400 = 3200; Third row: 6 × 20^1 = 6 × 20 = 120; Bottom row: 7 × 20^0 = 7 × 1 = 7.
4
Step 4: Sum all the calculated values: 2400 + 3200 + 120 + 7 = 3079.
Knowledge Points Involved
1
Mayan Numeral System
A vigesimal (base-20) positional numeral system used by the ancient Maya. Bars represent 5 units, dots represent 1 unit, and each vertical position corresponds to a power of 20, reading from bottom to top as 20^0, 20^1, 20^2, etc.
2
Positional Number Systems
A system where the value of a digit depends on its position (place value) relative to the decimal point (or base point). Different bases (like base-10, base-20) use different powers of the base for each place value.
3
Base Conversion (Base-20 to Base-10)
The process of converting a number from a non-base-10 system to base-10 by multiplying each digit by its corresponding base raised to the power of its place, then summing the products.
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