1. **State the problem:** Arrange the Roman numerals DXLVII, CCCXLVII, DCXXXVII, DCCXXXVII, CDXXXXVII in ascending order. 2. **Convert each Roman numeral to Arabic numbers:** - DXLVII: D=500, XL=40, VII=7, total = 500 + 40 + 7 = 547 - CCCXLVII: CCC=300, XL=40, VII=7, total = 300 + 40 + 7 = 347 - DCXXXVII: D=500, C=100, XXX=30, VII=7, total = 500 + 100 + 30 + 7 = 637 - DCCXXXVII: D=500, CC=200, XXX=30, VII=7, total = 500 + 200 + 30 + 7 = 737 - CDXXXXVII: CD=400, XXXX=40 (though not standard, treat as 40), VII=7, total = 400 + 40 + 7 = 447 3. **List the Arabic values:** 347, 447, 547, 637, 737 4. **Order the Arabic numbers ascending:** 347, 447, 547, 637, 737 5. **Match back to Roman numerals:** CCCXLVII, CDXXXXVII, DXLVII, DCXXXVII, DCCXXXVII 6. **Compare with options:** - Option a: CDXXXVII (437), DXLVII (547), CCCXLVII (347), DCXXXVII (637), DCCXXXVII (737) - incorrect order - Option b: CCCXLVII (347), CDXXXVII (437), DXLVII (547), DCXXXVII (637), DCCXXXVII (737) - matches correct order - Option c: CCCXLVII, DCXXXVII, DCCXXXVII, CDXXXVII, DXLVII - incorrect - Option d: DCCXXVII (727), DCXXXVII (637), DXLVII (547), CDXXXVII (437), CCCXLVII (347) - descending order - Option e: DXLVII, CCCXLVII, DCXXXVII, DCCXXXVII, CDXXXVII - incorrect **Final answer:** Option b is the correct ascending order.