Represent the following numbers using the Mayan system:

(i) 77 (ii) 100 (iii) 361 (iv) 721

Question

Represent the following numbers using the Mayan system: (i) 77 (ii) 100 (iii) 361 (iv) 721

Homi · Accepted Answer

We convert each number into Mayan numerals. We find the value for each vertical position.

Step 1 — Understanding Mayan Numerals

Mayan symbols are: dot (•) for 1, bar (—) for 5, and shell (O) for 0. We represent the shell symbol for zero as (O). Numbers are written vertically. Higher place values are at the top. Place values are 1, 20, 360 ( $20 \times 18$ ), 7200 ( $20^2 \times 18$ ), and so on. To convert, divide by the largest possible place value. Represent the quotient with Mayan symbols. Use the remainder for the next lower place value.

Step 2 — Representing 77

We start with the number 77. The largest place value less than or equal to 77 is 20. We divide 77 by 20. The quotient gives the value for the 20s place.

$77 \div 20 = 3 \text{ with a remainder of } 17$

The value for the 20s place is 3. We represent 3 using dots.

$3 = \text{•••}$

The remainder is 17. This value goes into the 1s place. We represent 17 using bars and dots.

$17 = (3 \times 5) + (2 \times 1)$

$17 = \text{===••}$

We place the symbols for 3 (20s place) above the symbols for 17 (1s place).

$\boxed{\begin{array}{c} \text{•••} \\ \text{===••} \end{array}}$

Diagram 1

Step 3 — Representing 100

We start with the number 100. The largest place value less than or equal to 100 is 20. We divide 100 by 20. The quotient gives the value for the 20s place.

$100 \div 20 = 5 \text{ with a remainder of } 0$

The value for the 20s place is 5. We represent 5 using a bar.

$5 = \text{—}$

The remainder is 0. This value goes into the 1s place. We represent 0 using the shell symbol.

$0 = \text{(O)}$

We place the symbols for 5 (20s place) above the symbols for 0 (1s place).

$\boxed{\begin{array}{c} \text{—} \\ \text{(O)} \end{array}}$

Diagram 2

Step 4 — Representing 361

We start with the number 361. The largest place value less than or equal to 361 is 360. We divide 361 by 360. The quotient gives the value for the 360s place.

$361 \div 360 = 1 \text{ with a remainder of } 1$

The value for the 360s place is 1. We represent 1 using a dot.

$1 = \text{•}$

The remainder is 1. Now we consider the 20s place. We divide 1 by 20. The quotient gives the value for the 20s place.

$1 \div 20 = 0 \text{ with a remainder of } 1$

The value for the 20s place is 0. We represent 0 using the shell symbol.

$0 = \text{(O)}$

The remainder is 1. This value goes into the 1s place. We represent 1 using a dot.

$1 = \text{•}$

We place the symbols for 1 (360s place) at the top, then 0 (20s place), then 1 (1s place) at the bottom.

$\boxed{\begin{array}{c} \text{•} \\ \text{(O)} \\ \text{•} \end{array}}$

Diagram 3

Step 5 — Representing 721

We start with the number 721. The largest place value less than or equal to 721 is 360. We divide 721 by 360. The quotient gives the value for the 360s place.

$721 \div 360 = 2 \text{ with a remainder of } 1$

The value for the 360s place is 2. We represent 2 using dots.

$2 = \text{••}$

The remainder is 1. Now we consider the 20s place. We divide 1 by 20. The quotient gives the value for the 20s place.

$1 \div 20 = 0 \text{ with a remainder of } 1$

The value for the 20s place is 0. We represent 0 using the shell symbol.

$0 = \text{(O)}$

The remainder is 1. This value goes into the 1s place. We represent 1 using a dot.

$1 = \text{•}$

We place the symbols for 2 (360s place) at the top, then 0 (20s place), then 1 (1s place) at the bottom.

$\boxed{\begin{array}{c} \text{••} \\ \text{(O)} \\ \text{•} \end{array}}$

Diagram 4

Answer

(i) The Mayan numeral for 77 is: $\begin{array}{c} \text{•••} \\ \text{===••} \end{array}$ (ii) The Mayan numeral for 100 is: $\begin{array}{c} \text{—} \\ \text{(O)} \end{array}$ (iii) The Mayan numeral for 361 is: $\begin{array}{c} \text{•} \\ \text{(O)} \\ \text{•} \end{array}$ (iv) The Mayan numeral for 721 is: $\begin{array}{c} \text{••} \\ \text{(O)} \\ \text{•} \end{array}$

Question 24

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