Chapter 5.CT, Problem 1CT

Write $3,685$ in Roman notation.

To determine

To write:

The numeral $3,685$ in Roman notation

Answer to Problem 1CT

Solution:

The Roman notation of numeral $3,685$ is $\text{MMMDCLXXXV}$

Explanation of Solution

Given information:

The numeral is $3,685$.

The given numeral $3,685$ can be written as $3000+600+80+5$.

Roman numeral $\text{M}$ represents $1,000$,

Roman numeral $\text{D}$ represents $500$,

Roman numeral $\text{C}$ represents $100$,

Roman numeral $\text{L}$ represents $50$,

Roman numeral $\text{X}$ represents $10$,

Roman numeral $\text{V}$ represents $5$.

$3,000$ is $3\times 1,000$.

$3,000$ is a combination of three $1,000$ s.

Roman numeral $\text{M}$ represents $1,000$.

So use $\text{MMM}$ for three $1,000$ s; therefore, $\text{MMM}$ represents $3,000$

$600$ is a combination of one $500$ and one $100$.

Roman numeral $\text{D}$ represents $500$.

Roman numeral $\text{C}$ represents $100$.

So, use $\text{D}$ for $500$ and $\text{C}$ for one $100$; therefore, $\text{DC}$ represents $600$

$80$ is a combination of one $50$ and three $10$ s.

Roman numeral $\text{L}$ represents $50$.

Roman numeral $\text{X}$ represents $10$.

So, use $\text{L}$ for $50$ and $\text{XXX}$ for three $10$ s; therefore, $\text{LXXX}$ represents $80$

Use $\text{V}$ for number $5$.

Therefore, $\begin{array}{cccc}3,000& 600& 80& 5\\ \downarrow & \downarrow & \downarrow & \downarrow \\ \text{MMM}& \text{DC}& \text{LXXX}& \text{V}\end{array}$.

Thus, the Roman notation for the number $3,685$ is $\text{MMMDCLXXXV}$.

Final statement:

Therefore, the Roman notation for the given numeral is $\text{MMMDCLXXXV}$.