Year 5: Roman numerals to 1,000 and years
Part of the Year 5 place value to 1,000,000 chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Roman numerals to 1,000 and years
In Year 4 you learned the Roman symbols I, V, X, L and C. To read numbers up to 1,000 you need two more: D = 500 and M = 1,000.
The rules. (1) Same symbols add up: XXX = 30. (2) A smaller symbol after a bigger one is added: DC = 500 + 100 = 600. (3) A smaller symbol before a bigger one is taken away: CM = 1,000 − 100 = 900. (4) Only I, X and C can be taken away, and only from the next two bigger symbols: I before V or X, X before L or C, C before D or M. (5) Never write the same symbol more than three times in a row. To write a number, do the thousands first, then the hundreds, then the tens, then the ones.
| Ones | Roman | Tens | Roman | Hundreds | Roman |
|---|---|---|---|---|---|
| 1 | I | 10 | X | 100 | C |
| 2 | II | 20 | XX | 200 | CC |
| 3 | III | 30 | XXX | 300 | CCC |
| 4 | IV | 40 | XL | 400 | CD |
| 5 | V | 50 | L | 500 | D |
| 6 | VI | 60 | LX | 600 | DC |
| 7 | VII | 70 | LXX | 700 | DCC |
| 8 | VIII | 80 | LXXX | 800 | DCCC |
| 9 | IX | 90 | XC | 900 | CM |
Years. Roman numerals are still used for years on buildings, films and TV programmes. The year 1999 is M + CM + XC + IX = MCMXCIX. The year 2026 is MM + XX + VI = MMXXVI. The Romans had no symbol for zero, so a zero in a number is simply left out: 2,006 has no tens or hundreds, so it is MMVI.
Key words. A numeral is a symbol for a number. Roman numerals use the letters I, V, X, L, C, D and M.
Key ideas
- I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000.
- Smaller after bigger: add. Smaller before bigger: take away (IV, IX, XL, XC, CD, CM).
- Never more than three of the same symbol in a row.
- Write thousands, then hundreds, then tens, then ones: 1,994 = M + CM + XC + IV = MCMXCIV.
- A zero is left out. There is no Roman symbol for zero.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.CD = 500 − 100 = 400 (small symbol in front, so take it away)
XL = 50 − 10 = 40 (small symbol in front, so take it away)
V = 5
I = 1
I = 1 - Add the values. Add the biggest groups first.400 + 40 + 5 + 1 + 1 = 447
- Write the answer. 447
Check. Write 447 in Roman numerals: CD + XL + VII = CDXLVII. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
M = 1,000
X = 10
X = 10
V = 5
I = 1 - Add the values. Add the biggest groups first.1,000 + 1,000 + 10 + 10 + 5 + 1 = 2,026
- Write the answer. 2026
Check. Write 2,026 in Roman numerals: MM + XX + VI = MMXXVI. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.649 = 600 + 40 + 9
- Write 600 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).600 = DC
- Write 40 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).40 = XL
- Write 9 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).9 = IX
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.DC + XL + IX = DCXLIX
Check. Read it back: 500 + 100 + 40 + 9 = 649. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,994 = 1,000 + 900 + 90 + 4
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Write 900 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).900 = CM
- Write 90 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).90 = XC
- Write 4 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).4 = IV
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M + CM + XC + IV = MCMXCIV
Check. Read it back: 1,000 + 900 + 90 + 4 = 1,994. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,066 = 1,000 + 60 + 6
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Write 60 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).60 = LX
- Write 6 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).6 = VI
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M + LX + VI = MLXVI
Check. Read it back: 1,000 + 50 + 10 + 5 + 1 = 1,066. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
D = 500
C = 100
C = 100
C = 100
XC = 100 − 10 = 90 (small symbol in front, so take it away)
V = 5 - Add the values. Add the biggest groups first.1,000 + 500 + 100 + 100 + 100 + 90 + 5 = 1,895
- Write the answer. 1895
Check. Write 1,895 in Roman numerals: M + DCCC + XC + V = MDCCCXCV. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change DLXII into a number. Split it into groups and add.DLXII = D (500) + L (50) + X (10) + I (1) + I (1) = 562
- Change CXXXVIII into a number. Do the same.CXXXVIII = C (100) + X (10) + X (10) + X (10) + V (5) + I (1) + I (1) + I (1) = 138
- Do the calculation. Use our normal numbers.562 + 138 = 700
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.700 = DCC = DCC
Check. Read DCC again: 500 + 100 + 100 = 700. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change CM into a number. Split into groups and add.CM = 900
- Change DCCLXXXVIII into a number. Do the same.DCCLXXXVIII = 788
- Compare the numbers. Compare from the left, as usual.900 > 788
- Write the answer with the Roman numerals. CM > DCCLXXXVIII
Check. CM is 112 more than DCCLXXXVIII. ✓
Watch out. Do not compare the number of letters. A short numeral like CM (900) can be bigger than a long one like DCCLXXXVIII (788).
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numeral into a year in digits, then take it away from the later year.
- Change MCMLXIX into a year. Split it into groups and add.MCMLXIX = M (1000) + CM (1000 − 100) + L (50) + X (10) + IX (10 − 1) = 1969
- Decide which year is later. The later year is the bigger number. We take the earlier year away from it.1969 < 2026
- Subtract from the later year. 2026 is the later year.2026 − 1969 = 57
Check. 1969 + 57 = 2026. ✓
Watch out. Write the years as ordinary numbers before you subtract.
Watch out
Do not write 49 as IL or 99 as IC. I can only go before V or X, so 49 is XL + IX = XLIX and 99 is XC + IX = XCIX. And do not write 4 as IIII or 900 as DCCCC: they are IV and CM. Never put the same symbol more than three times in a row.Exercise 1F Roman numerals
Non-calculatorKey words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.C = 100
L = 50
IX = 10 − 1 = 9 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.100 + 50 + 9 = 159
- Write the answer. 159
Check. Write 159 in Roman numerals: C + L + IX = CLIX. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.D = 500
XL = 50 − 10 = 40 (small symbol in front, so take it away)
IV = 5 − 1 = 4 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.500 + 40 + 4 = 544
- Write the answer. 544
Check. Write 544 in Roman numerals: D + XL + IV = DXLIV. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.CM = 1000 − 100 = 900 (small symbol in front, so take it away)
XC = 100 − 10 = 90 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.900 + 90 = 990
- Write the answer. 990
Check. Write 990 in Roman numerals: CM + XC = CMXC. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.D = 500
C = 100
C = 100
C = 100
L = 50
X = 10
X = 10
X = 10
V = 5
I = 1
I = 1
I = 1 - Add the values. Add the biggest groups first.500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 + 1 = 888
- Write the answer. 888
Check. Write 888 in Roman numerals: DCCC + LXXX + VIII = DCCCLXXXVIII. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.CD = 500 − 100 = 400 (small symbol in front, so take it away)
XL = 50 − 10 = 40 (small symbol in front, so take it away)
IX = 10 − 1 = 9 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.400 + 40 + 9 = 449
- Write the answer. 449
Check. Write 449 in Roman numerals: CD + XL + IX = CDXLIX. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
CD = 500 − 100 = 400 (small symbol in front, so take it away)
L = 50
X = 10 - Add the values. Add the biggest groups first.1,000 + 400 + 50 + 10 = 1,460
- Write the answer. 1,460
Check. Write 1,460 in Roman numerals: M + CD + LX = MCDLX. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.134 = 100 + 30 + 4
- Write 100 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).100 = C
- Write 30 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).30 = XXX
- Write 4 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).4 = IV
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.C + XXX + IV = CXXXIV
Check. Read it back: 100 + 10 + 10 + 10 + 4 = 134. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.478 = 400 + 70 + 8
- Write 400 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).400 = CD
- Write 70 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).70 = LXX
- Write 8 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).8 = VIII
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.CD + LXX + VIII = CDLXXVIII
Check. Read it back: 400 + 50 + 10 + 10 + 5 + 1 + 1 + 1 = 478. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.909 = 900 + 9
- Write 900 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).900 = CM
- Write 9 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).9 = IX
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.CM + IX = CMIX
Check. Read it back: 900 + 9 = 909. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.640 = 600 + 40
- Write 600 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).600 = DC
- Write 40 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).40 = XL
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.DC + XL = DCXL
Check. Read it back: 500 + 100 + 40 = 640. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.999 = 900 + 90 + 9
- Write 900 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).900 = CM
- Write 90 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).90 = XC
- Write 9 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).9 = IX
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.CM + XC + IX = CMXCIX
Check. Read it back: 900 + 90 + 9 = 999. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,000 is just one part
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M = M
Check. Read it back: 1,000 = 1,000. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.400 is just one part
- Write 400 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).400 = CD
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.CD = CD
Check. Read it back: 400 = 400. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.500 is just one part
- Write 500 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).500 = D
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.D = D
Check. Read it back: 500 = 500. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.900 is just one part
- Write 900 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).900 = CM
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.CM = CM
Check. Read it back: 900 = 900. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.600 is just one part
- Write 600 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).600 = DC
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.DC = DC
Check. Read it back: 500 + 100 = 600. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.90 is just one part
- Write 90 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).90 = XC
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.XC = XC
Check. Read it back: 90 = 90. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,000 is just one part
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M = M
Check. Read it back: 1,000 = 1,000. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
CM = 1000 − 100 = 900 (small symbol in front, so take it away)
L = 50
X = 10
X = 10
X = 10
IV = 5 − 1 = 4 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.1,000 + 900 + 50 + 10 + 10 + 10 + 4 = 1,984
- Write the answer. 1984
Check. Write 1,984 in Roman numerals: M + CM + LXXX + IV = MCMLXXXIV. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
D = 500
C = 100
L = 50
X = 10
V = 5
I = 1 - Add the values. Add the biggest groups first.1,000 + 500 + 100 + 50 + 10 + 5 + 1 = 1,666
- Write the answer. 1666
Check. Write 1,666 in Roman numerals: M + DC + LX + VI = MDCLXVI. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
C = 100
C = 100
X = 10
V = 5 - Add the values. Add the biggest groups first.1,000 + 100 + 100 + 10 + 5 = 1,215
- Write the answer. 1215
Check. Write 1,215 in Roman numerals: M + CC + X + V = MCCXV. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
M = 1,000
X = 10
X = 10
IV = 5 − 1 = 4 (small symbol in front, so take it away) - Add the values. Add the biggest groups first.1,000 + 1,000 + 10 + 10 + 4 = 2,024
- Write the answer. 2024
Check. Write 2,024 in Roman numerals: MM + XX + IV = MMXXIV. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the Roman numeral into groups, write the value of each group, then add them up.
- Split the numeral into groups, reading from the left. A small symbol in front of a bigger one (like CM, XC or IV) is taken away. Otherwise just add.M = 1,000
CM = 1000 − 100 = 900 (small symbol in front, so take it away)
X = 10
I = 1
I = 1 - Add the values. Add the biggest groups first.1,000 + 900 + 10 + 1 + 1 = 1,912
- Write the answer. 1912
Check. Write 1,912 in Roman numerals: M + CM + X + II = MCMXII. ✓
Watch out. Read from the left. A small symbol is only taken away when it comes BEFORE a bigger one: IX is 9 but XI is 11.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,066 = 1,000 + 60 + 6
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Write 60 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).60 = LX
- Write 6 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).6 = VI
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M + LX + VI = MLXVI
Check. Read it back: 1,000 + 50 + 10 + 5 + 1 = 1,066. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,666 = 1,000 + 600 + 60 + 6
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Write 600 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).600 = DC
- Write 60 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).60 = LX
- Write 6 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).6 = VI
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M + DC + LX + VI = MDCLXVI
Check. Read it back: 1,000 + 500 + 100 + 50 + 10 + 5 + 1 = 1,666. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.1,948 = 1,000 + 900 + 40 + 8
- Write 1,000 in Roman numerals. M is 1,000.1,000 = M
- Write 900 in Roman numerals. D is 500; 400 is CD (100 before 500) and 900 is CM (100 before 1,000).900 = CM
- Write 40 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).40 = XL
- Write 8 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).8 = VIII
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.M + CM + XL + VIII = MCMXLVIII
Check. Read it back: 1,000 + 900 + 40 + 5 + 1 + 1 + 1 = 1,948. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Split the number into thousands, hundreds, tens and ones. Write each part in Roman numerals, then put them side by side (biggest first).
- Split the number into thousands, hundreds, tens and ones. Roman numerals are built one part at a time, biggest first.2,026 = 2,000 + 20 + 6
- Write 2,000 in Roman numerals. M is 1,000.2,000 = MM
- Write 20 in Roman numerals. 40 is XL (10 before 50) and 90 is XC (10 before 100).20 = XX
- Write 6 in Roman numerals. 4 is IV (1 before 5) and 9 is IX (1 before 10).6 = VI
- Put the parts side by side, biggest first. Thousands on the left, then hundreds, tens and ones.MM + XX + VI = MMXXVI
Check. Read it back: 1,000 + 1,000 + 10 + 10 + 5 + 1 = 2,026. ✓
Watch out. Never write the same symbol more than three times in a row. 4 is IV, not IIII; 40 is XL; 400 is CD; 900 is CM.
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change CDXL into a number. Split into groups and add.CDXL = 440
- Change CCCXLIV into a number. Do the same.CCCXLIV = 344
- Compare the numbers. Compare from the left, as usual.440 > 344
- Write the answer with the Roman numerals. CDXL > CCCXLIV
Check. CDXL is 96 more than CCCXLIV. ✓
Watch out. Do not compare the number of letters. A short numeral like CM (900) can be bigger than a long one like DCCLXXXVIII (788).
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change DCCLXXXIX into a number. Split into groups and add.DCCLXXXIX = 789
- Change DCCXC into a number. Do the same.DCCXC = 790
- Compare the numbers. Compare from the left, as usual.789 < 790
- Write the answer with the Roman numerals. DCCLXXXIX < DCCXC
Check. DCCLXXXIX is 1 less than DCCXC. ✓
Watch out. Do not compare the number of letters. A short numeral like CM (900) can be bigger than a long one like DCCLXXXVIII (788).
Method. Change both Roman numerals into numbers. Then compare the numbers.
- Change CM into a number. Split into groups and add.CM = 900
- Change DCCCXCIX into a number. Do the same.DCCCXCIX = 899
- Compare the numbers. Compare from the left, as usual.900 > 899
- Write the answer with the Roman numerals. CM > DCCCXCIX
Check. CM is 1 more than DCCCXCIX. ✓
Watch out. Do not compare the number of letters. A short numeral like CM (900) can be bigger than a long one like DCCLXXXVIII (788).
Method. Change each Roman numeral into a number, order the numbers, then write the Roman numerals in that order.
- Change each to a number. Split into groups and add.DCLXVI = 666
DCXLIX = 649
DLXVI = 566
DCC = 700
CMXC = 990 - Order the numbers. Compare from the left (hundreds first).566, 649, 666, 700, 990
- Write the Roman numerals in that order. DLXVI, DCXLIX, DCLXVI, DCC, CMXC
Check. There are 5 numerals in the question and 5 in the answer. ✓
Watch out. Write the answer in Roman numerals, because that is what the question asks for.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change XC into a number. Split it into groups and add.XC = XC (100 − 10) = 90
- Change CCX into a number. Do the same.CCX = C (100) + C (100) + X (10) = 210
- Do the calculation. Use our normal numbers.90 + 210 = 300
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.300 = CCC = CCC
Check. Read CCC again: 100 + 100 + 100 = 300. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change DL into a number. Split it into groups and add.DL = D (500) + L (50) = 550
- Change CCCXV into a number. Do the same.CCCXV = C (100) + C (100) + C (100) + X (10) + V (5) = 315
- Do the calculation. Use our normal numbers.550 + 315 = 865
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.865 = DCCC + LX + V = DCCCLXV
Check. Read DCCCLXV again: 500 + 100 + 100 + 100 + 50 + 10 + 5 = 865. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change M into a number. Split it into groups and add.M = M (1000) = 1,000
- Change CDXL into a number. Do the same.CDXL = CD (500 − 100) + XL (50 − 10) = 440
- Do the calculation. Use our normal numbers.1,000 − 440 = 560
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.560 = D + LX = DLX
Check. Read DLX again: 500 + 50 + 10 = 560. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change DCCC into a number. Split it into groups and add.DCCC = D (500) + C (100) + C (100) + C (100) = 800
- Change CCLXV into a number. Do the same.CCLXV = C (100) + C (100) + L (50) + X (10) + V (5) = 265
- Do the calculation. Use our normal numbers.800 − 265 = 535
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.535 = D + XXX + V = DXXXV
Check. Read DXXXV again: 500 + 10 + 10 + 10 + 5 = 535. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numerals into numbers, do the calculation, then change the answer back into Roman numerals.
- Change CMXC into a number. Split it into groups and add.CMXC = CM (1000 − 100) + XC (100 − 10) = 990
- Change DLX into a number. Do the same.DLX = D (500) + L (50) + X (10) = 560
- Do the calculation. Use our normal numbers.990 − 560 = 430
- Change the answer back to Roman numerals. Thousands, hundreds, tens, then ones.430 = CD + XXX = CDXXX
Check. Read CDXXX again: 400 + 10 + 10 + 10 = 430. ✓
Watch out. Roman numerals are hard to add directly. Change them to numbers first.
Key words. Roman numerals are letters used for numbers: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. A small symbol before a bigger one is taken away; after it is added.
Method. Change the Roman numeral into a year in digits, then take it away from the later year.
- Change MCMXCIV into a year. Split it into groups and add.MCMXCIV = M (1000) + CM (1000 − 100) + XC (100 − 10) + IV (5 − 1) = 1994
- Decide which year is later. The later year is the bigger number. We take the earlier year away from it.1994 < 2026
- Subtract from the later year. 2026 is the later year.2026 − 1994 = 32
Check. 1994 + 32 = 2026. ✓
Watch out. Write the years as ordinary numbers before you subtract.
Method. Change both Roman numerals into numbers. Then take away to find how much longer.
- Change CCCLXXV to a number. CCC = 300, L = 50, XX = 20 and V = 5.CCCLXXV = 300 + 50 + 20 + 5 = 375
- Change DXL to a number. D = 500 and XL = 50 − 10 = 40.DXL = 500 + 40 = 540
- Find the difference. The second road is longer, so take the shorter from the longer.540 − 375 = 165 km
Check. 375 + 165 = 540. ✓
Watch out. Write both lengths as ordinary numbers before you take away.
Method. Work out each number properly using the rules: thousands, hundreds, tens, then ones.
- Write 1,999. 1,999 = 1,000 + 900 + 90 + 9.M + CM + XC + IX = MCMXCIX
- Write 490. 490 = 400 + 90.CD + XC = CDXC
- Say what went wrong. Tom took 1 away from 1,000 and 10 away from 500. But I can only go in front of V or X, and X can only go in front of L or C. So each part must be written separately.The correct numerals are MCMXCIX and CDXC.
Check. 1,000 + 900 + 90 + 9 = 1,999 and 400 + 90 = 490. ✓
Watch out. Break the number into thousands, hundreds, tens and ones. Write each part, then join them.
Method. Check each numeral against the rules. Rule 1: never more than three of the same symbol in a row. Rule 2: only I, X and C are taken away, and only from the next two bigger symbols.
- Check each numeral. Look at the repeats and at the small symbols in front of bigger ones.XXXX: wrong
MCMXCIX: correct (= 1,999)
VX: wrong
XCIV: correct (= 94)
IL: wrong - Explain each mistake. Use the rules.XXXX: There are four Xs in a row. We never write more than three of the same symbol in a row. 40 is XL.
VX: V (5) is never taken away from another symbol. Only I, X and C go in front to take away. 5 is just V.
IL: I can only go in front of V or X. To make 49 you write 40 + 9 = XL + IX = XLIX. - Write the answer. XXXX, VX and IL
Check. MCMXCIX = 1,999 and XCIV = 94 are both written correctly. ✓
Watch out. A short numeral can be correct and a short numeral can be wrong. Check the rules, not the length.
Method. The thousands, hundreds, tens and ones each use the most letters when they have the most repeated symbols. Think about which hundreds, tens and ones are longest.
- Thousands. Every year from 1000 to 1999 starts with just M. The years 2000 to 2026 start with MM, but they have no hundreds and only small tens, so they are short (7 letters at most). So the longest year is between 1000 and 1999.M = 1 letter
- Hundreds. DCCC (800) has 4 letters. No other hundreds digit has more.DCCC = 4 letters
- Tens. LXXX (80) has 4 letters.LXXX = 4 letters
- Ones. VIII (8) has 4 letters.VIII = 4 letters
- Put them together. Add the letters.1 + 4 + 4 + 4 = 13 → MDCCCLXXXVIII (1888)
Check. Only 1888 gives 13 letters. The next longest years, like 1878, have 12 letters. ✓
Watch out. Numerals with a 4 or a 9 (like IV or CM) are short. The longest use 8s.