Loading…
Math Tutor's Solution: 166 in Roman Numerals is CLXVI
Methods
Learn from a Math Tutor: How do Roman Numerals Work?
Your math tutor here! Let’s dive into Roman numerals. Used widely until the 14th century, this number system was a go-to for people in Western cultures. Eventually, it was replaced by the Hindu-Arabic system, which made math and calculations much easier.
But Roman numerals are still around today!
They’re based on a set of letters—like X, V, and D—that each represent a specific number. Let’s break it down with a list of the seven key letters and their numerical values.
To get a head start on how these work, take a look at this next table - it has many common numbers that are used to convert regular numbers to Roman Numerals or vice-versa. With some help from the table above, can you identify any patterns? What rules do you think they’re using?
If you’ve gone through these tables, you might have realized what some of the rules are. If not, you will find the rules that one needs to abide by in order to write any number as a Roman Numeral successfully:
If you want a number that is a multiple of one of the 7 letters they use, its value is the sum of the value of that letter and how many times it appears. For example, III = 3 because we repeated three I’s and I is 1.
- Letters I, X, and C can be repeated a maximum of three times but not four or more. For example: XX = 20 because X = 10, so 10 + 10 = 20 = XX
- Letters L, V, D, cannot be repeated at all - they must be unique for that number.
- When you write a letter with a smaller value before a letter with a bigger value, you must subtract the smaller value from the bigger value. For example, IV is 4 because I = 1, V = 5, and since the letter I came before V, we must subtract: IV = 5 - 1 = 4.
- When you write a letter with a smaller value after a letter with a bigger value, you must add the smaller value to the bigger value. For example, LX is 60 because L = 50, X = 10, and since X is after L, we must add: LX = 50 + 10 = 60
- The letter I can be subtracted from V and X only and the letter X can only be subtracted from L, M and C.
Step-by-step from Math Tutor: Converting 166 in Roman Numerals
Using the above rules and the basic 7 letters of the modern Roman Numerals, we can break down 166 into the following:
166 = 100 + 50 + 10 + 5 + 1 = CLXVI
As you can see, we can break down 166 by seeing which of the biggest numbers fit and then finding smaller ones to add up to/subtract while following the given rules. As a result, we see that 166 in Roman Numerals is CLXVI.
Math Tutor Suggests: More Roman Numerals Math Problem Practice
Check out these other problems of converting regular numbers to Roman Numerals:
Download FREE Math Resources
Take advantage of our free downloadable resources and study materials for at-home learning.
8 Math Hacks and Tricks to Turn Your 'Okay' Math Student Into a Math Champion!
One thing we teach our students at Thinkster is that there are multiple ways to solve a math problem. This helps our students learn to think flexibly and non-linearly.
Get PDF
Math Tutoring to Boost Your Child’s Math Skills & Scores by 90% in Just 3 Months – Guaranteed!
Does your child struggle with math homework or understanding tricky math concepts? Do they do okay in math, but express excitement to learn new material or advanced math?
A Thinkster Math tutor provides one-to-one support to help elementary, middle school, and high school students build confidence and master math subjects like K-8 math, pre-algebra, algebra, geometry, calculus, and more.
Our expert math tutors customize math lessons to your child’s unique needs, making learning math fun and effective. We help students improve grades, develop strong critical thinking skills through solving word problems, excel in standardized tests, and develop strong problem-solving skills.
Our expert math tutors are ready to help make your child a champion and develop strong math mastery! Sign up for our 7-day free trial and get the best math tutor for your child today!
Start 7-Day Free Trial