roman numerals

Roman numerals are written as combinations of the seven letters in the table below. The letters can be written as capital (XVI) or lower-case letters (xvi).

Roman Numerals I = 1 C = 100 V = 5 D = 500 X = 10 M = 1000 L = 50

You can use a roman numerals chart or conversion table to lookup Roman numerals or you can easily learn how to calculate them yourself with a few simple rules.

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How to Translate Roman Numerals

If smaller numbers follow larger numbers, the numbers are added. If a smaller number precedes a larger number, the smaller number is subtracted from the larger. For example, if you want to say 1,100 in Roman numerals, you would say M for 1000 and then put a C after it for 100; in other words 1,100=MC in Roman numerals.

Some more examples:

• VIII = 5+3 = 8
• IX = 10-1 = 9
• XL = 50-10 = 40
• XC = 100-10 = 90
• MCMLXXXIV = 1000+(1000-100)+50+30+(5-1) = 1984

Roman Numeral Table 1 I 14 XIV 27 XXVII 150 CL 2 II 15 XV 28 XXVIII 200 CC 3 III 16 XVI 29 XXIX 300 CCC 4 IV 17 XVII 30 XXX 400 CD 5 V 18 XVIII 31 XXXI 500 D 6 VI 19 XIX 40 XL 600 DC 7 VII 20 XX 50 L 700 DCC 8 VIII 21 XXI 60 LX 800 DCCC 9 IX 22 XXII 70 LXX 900 CM 10 X 23 XXIII 80 LXXX 1000 M 11 XI 24 XXIV 90 XC 1600 MDC 12 XII 25 XXV 100 C 1700 MDCC 13 XIII 26 XXVI 101 CI 1900 MCM

A Brief History of Roman Numerals

What is the history of Roman numerals? Roman numerals, as the name suggests, originated in ancient Rome. No one is sure when Roman numerals were first used, but they far predate the middle ages. Theories abound as to the origins of this counting system, but it is commonly believed to have started with the ancient Etruscans. The symbol for one in the Roman numeral system probably represented a single tally mark of the kind people would notch into wood or dirt to keep track of items or events they were counting.

Roman Numerals in Modern Times

Roman numerals are still used today in a variety of applications. If you are creating an outline for a story or report, you will be expected to use Roman numerals. They are also commonly used on clocks and watches, in books to number prefaces, forwards and book chapters as well as on films and big events. Monarchs and popes are usually numbered with this system as are guitar chords and the cranial nerves.

Roman Numerals in Crosswords

Crossword puzzle creators are fond of using Roman numerals in their puzzles, ranging from requiring translation of complex numbers to expecting puzzlers to know that a Roman numeral M stands for one thousand. If you want to be an expert crossword puzzler, you probably need to get familiar with the Roman numeral conversion process or keep a conversion chart handy. A typical crossword clue is "Half of MCIV" which should be answered "DLII".

Resources

multiplying decimals

Here are the rules for multiplying decimal numbers:

1. Multiply the numbers just as if they were whole numbers:

• Line up the numbers on the right--do not align the decimal points.
• Starting on the right, multiply each digit in the top number by each digit in the bottom number, just as with whole numbers.
• Add the products.

2. Place the decimal point in the answer by starting at the right and moving the point the number of places equal to the sum of the decimal places in both numbers multiplied.

37.7 x 2.8 = ? --->
     37.7     ( 1 decimal place )
   x  2.8     ( 1 decimal place )
  3016
+754 
105.56       ( 2 decimal places, move point 2 places left )

Hint: Use estimating to help you check the placement of the decimal point. You could round 37.7 to 40 and 2.8 to 3. It's easy to multiply 3 x 40 so you know your answer should be close to 120.

Here's a "mental math" shortcut: When multiplying a number by a multiple of ten, just move the decimal point one space to the right for every zero.
10 x 0.6284 = 6.284 (1 zero, 1 space right)
100 x 0.6284 = 62.84 (2 zeroes, 2 spaces right)
1000 x 0.6284 = 628.4 (3 zeroes, 3 spaces right)
10,000 x 0.6284 = 6284 (4 zeroes, 4 spaces right)
100,000 x 0.6284 = 62,840 (5 zeroes, 5 spaces right)
Example

1. Find the product of    9.683 x 6.1 = ?Line up the numbers on the right, multiply each digit in the top number by the each digit in the bottom number (like whole numbers), add the products, and mark off decimal places equal to the sum of the decimal places in the numbers being multiplied.
        9.683    ( 3 decimal places)
        x  6.1   ( 1 decimal place)
         9683   (1 x 9683)
   + 58098     (6 x 96830)
      59.0663  (3 + 1 = 4 decimal places)

2. Jackie just bought a new convertible. How far will she get on the highway before she runs out of gas and has to call a tow truck?First, estimate your answer to the tens place. Then make an exact calculation, using the calculator.
   Estimate:
   24.5 -> 20 15.2 -> 20 20 x 20 = 400 miles
   Exact calculation:

24.5 x 15.2 = 372.40

You can drop the trailing zero in a decimal number. For example, 372.40 is the same as 372.4. This is because the ".40" part of the number is the same as ".4". This is the same as saying that 40/100 is the same as 4/10.

properties of addition

Properties of Addition

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.

Commutative property: When two numbers are added, the sum is the same regardless of the order of the addends. For example 4 + 2 = 2 + 4

Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example (2 + 3) + 4 = 2 + (3 + 4)

Additive Identity Property: The sum of any number and zero is the original 

number. For example 5 + 0 = 5.

Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 4*6 + 4*3

decimals to fractions

Decimals to FractionsDecimals to Fractions

(Multiply top and bottom by 10 until you get a whole number, then simplify)

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75

1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100
0.75	=	75
1		100
× 100

(Do you see how it turns the top number 
into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

	÷5		÷ 5
75	=	15	=	3
100		20		4
	÷5		÷ 5

Answer = ³/₄

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Example: Express 0.625 as a fraction

Step 1: write down:

0.625

1

Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

625

1,000

Step 3: Simplify the fraction (it took me two steps here):

	÷ 25		÷ 5
625	=	25	=	5
1,000		40		8
	÷ 25		÷ 5

Answer = ⁵/₈

Example: Express 0.333 as a fraction

Step 1: Write down:

0.333

1

Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

333

1,000

Step 3: Simplify Fraction:

Can't get any simpler!

Answer = ³³³/_1,000

But a Special Note:

If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In this case we would write down:

0.333...

1

Then MULTIPLY both top and bottom by 3:

× 3
0.333...	=	0.999...
1		3
× 3

And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:

(Multiply top and bottom by 10 until you get a whole number, then simplify)

To convert a Decimal to a Fraction follow these steps:

Step 1: Write down the decimal divided by 1, like this: decimal/1

Step 2: Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

Step 3: Simplify (or reduce) the fraction

Example: Express 0.75 as a fraction

Step 1: Write down 0.75 divided by 1:

0.75

1

Step 2: Multiply both top and bottom by 100 (there were 2 digits after the decimal point so that is 10×10=100):

× 100
0.75	=	75
1		100
× 100

(Do you see how it turns the top number 
into a whole number?)

Step 3: Simplify the fraction (this took me two steps):

	÷5		÷ 5
75	=	15	=	3
100		20		4
	÷5		÷ 5

Answer = ³/₄

Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !

Example: Express 0.625 as a fraction

Step 1: write down:

0.625

1

Step 2: multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

625

1,000

Step 3: Simplify the fraction (it took me two steps here):

	÷ 25		÷ 5
625	=	25	=	5
1,000		40		8
	÷ 25		÷ 5

Answer = ⁵/₈

Example: Express 0.333 as a fraction

Step 1: Write down:

0.333

1

Step 2: Multiply both top and bottom by 1,000 (there were 3 digits after the decimal point so that is 10×10×10=1,000)

333

1,000

Step 3: Simplify Fraction:

Can't get any simpler!

Answer = ³³³/_1,000

But a Special Note:

If you really meant 0.333... (in other words 3s repeating forever which is called 3 recurring) then we need to follow a special argument. In this case we would write down:

0.333...

1

Then MULTIPLY both top and bottom by 3:

× 3
0.333...	=	0.999...
1		3
× 3

And 0.999... = 1 (Does it? - see the 9 Recurring discussion for more if you are interested), so:

Answer = 1/3