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Convert the following Hindu-Arabic numerals to Roman numerals: 38, 221, 1000, 110, 175, 836.

Mathematics

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Step-by-step solution

28 steps

Here are the Hindu-Arabic numerals converted to Roman numerals:

1) 38

  1. Break down the number by place value.

    38=30+838 = 30 + 8
  2. Convert each part to Roman numerals.

    30=XXX30 = \text{XXX} 8=VIII8 = \text{VIII}
  3. Combine the Roman numerals.

    38=XXXVIII38 = \text{XXXVIII}

    The Roman numeral for 38 is XXXVIII\boxed{\text{XXXVIII}}.

    2) 221

  4. Break down the number by place value.

    221=200+20+1221 = 200 + 20 + 1
  5. Convert each part to Roman numerals.

    200=CC200 = \text{CC} 20=XX20 = \text{XX} 1=I1 = \text{I}
  6. Combine the Roman numerals.

    221=CCXXI221 = \text{CCXXI}

    The Roman numeral for 221 is CCXXI\boxed{\text{CCXXI}}.

    3) 1,000

  7. Convert the number to its Roman numeral equivalent.

    1000=M1000 = \text{M}

    The Roman numeral for 1,000 is M\boxed{\text{M}}.

    4) 110

  8. Break down the number by place value.

    110=100+10110 = 100 + 10
  9. Convert each part to Roman numerals.

    100=C100 = \text{C} 10=X10 = \text{X}
  10. Combine the Roman numerals.

    110=CX110 = \text{CX}

    The Roman numeral for 110 is CX\boxed{\text{CX}}.

    5) 175

  11. Break down the number by place value.

    175=100+70+5175 = 100 + 70 + 5
  12. Convert each part to Roman numerals.

    100=C100 = \text{C} 70=LXX70 = \text{LXX} 5=V5 = \text{V}
  13. Combine the Roman numerals.

    175=CLXXV175 = \text{CLXXV}

    The Roman numeral for 175 is CLXXV\boxed{\text{CLXXV}}.

    6) 836

  14. Break down the number by place value.

    836=800+30+6836 = 800 + 30 + 6
  15. Convert each part to Roman numerals.

    800=DCCC800 = \text{DCCC} 30=XXX30 = \text{XXX} 6=VI6 = \text{VI}
  16. Combine the Roman numerals.

    836=DCCCXXXVI836 = \text{DCCCXXXVI}

    The Roman numeral for 836 is DCCCXXXVI\boxed{\text{DCCCXXXVI}}.

    7) 99

  17. Break down the number by place value.

    99=90+999 = 90 + 9
  18. Convert each part to Roman numerals using subtraction rule.

    90=XC(100−10)90 = \text{XC} \quad (100 - 10) 9=IX(10−1)9 = \text{IX} \quad (10 - 1)
  19. Combine the Roman numerals.

    99=XCIX99 = \text{XCIX}

    The Roman numeral for 99 is XCIX\boxed{\text{XCIX}}.

    8) 217

  20. Break down the number by place value.

    217=200+10+7217 = 200 + 10 + 7
  21. Convert each part to Roman numerals.

    200=CC200 = \text{CC} 10=X10 = \text{X} 7=VII7 = \text{VII}
  22. Combine the Roman numerals.

    217=CCXVII217 = \text{CCXVII}

    The Roman numeral for 217 is CCXVII\boxed{\text{CCXVII}}.

    9) 590

  23. Break down the number by place value.

    590=500+90590 = 500 + 90
  24. Convert each part to Roman numerals using subtraction rule for 90.

    500=D500 = \text{D} 90=XC(100−10)90 = \text{XC} \quad (100 - 10)
  25. Combine the Roman numerals.

    590=DXC590 = \text{DXC}

    The Roman numeral for 590 is DXC\boxed{\text{DXC}}.

    10) 384

  26. Break down the number by place value.

    384=300+80+4384 = 300 + 80 + 4
  27. Convert each part to Roman numerals using subtraction rule for 4.

    300=CCC300 = \text{CCC} 80=LXXX80 = \text{LXXX} 4=IV(5−1)4 = \text{IV} \quad (5 - 1)
  28. Combine the Roman numerals.

    384=CCCLXXXIV384 = \text{CCCLXXXIV}

    The Roman numeral for 384 is CCCLXXXIV\boxed{\text{CCCLXXXIV}}.

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