This homework solution contains questions about number systems and their properties. It asks to find the predecessor of the smallest 5-digit number and to convert between Roman and Hindu-Arabic numera

The smallest 5-digit number is 10000.

The predecessor is one less than the number.

The predecessor of the smallest 5-digit number is $\boxed{\text{9999}}$.

Q1: Write the following Roman numerals in Hindu-Arabic numerals.

• a) IX = $\boxed{\text{9}}$
• b) XIV = $\boxed{\text{14}}$
• c) XX = $\boxed{\text{20}}$
• d) XXVII = $\boxed{\text{27}}$
• e) XXX = $\boxed{\text{30}}$
• f) XL = $\boxed{\text{40}}$
• g) XLV = $\boxed{\text{45}}$
• h) XIX = $\boxed{\text{19}}$
• i) XXXVIII = $\boxed{\text{38}}$
• j) XLIX = $\boxed{\text{49}}$

Q2: Write the following Hindu-Arabic numerals in Roman numerals.

• a) 5 = $\boxed{\text{V}}$
• b) 12 = $\boxed{\text{XII}}$
• c) 18 = $\boxed{\text{XVIII}}$
• d) 24 = $\boxed{\text{XXIV}}$
• e) 29 = $\boxed{\text{XXIX}}$
• f) 31 = $\boxed{\text{XXXI}}$
• g) 36 = $\boxed{\text{XXXVI}}$
• h) 44 = $\boxed{\text{XLIV}}$
• i) 47 = $\boxed{\text{XLVII}}$
• j) 50 = $\boxed{\text{L}}$

Q3: Fill in the blanks.

• a) We cannot repeat any roman number more than $\boxed{\text{three}}$ times.
• b) Roman numeral for 0 is $\boxed{\text{not defined}}$.
• c) Only $\boxed{\text{I}}$, $\boxed{\text{X}}$, $\boxed{\text{C}}$, and $\boxed{\text{M}}$ can be repeated.
• d) XL means $\boxed{\text{40}}$.
• e) Roman numeral for 49 is $\boxed{\text{XLIX}}$.
• f) XX + X = $\boxed{\text{XXX}}$.
• g) Roman numeral for 19 is $\boxed{\text{XIX}}$.
• h) $\boxed{\text{XXXV}}$ is the Roman numeral for 35.

Q4: Write the predecessor and successor of the following Roman numerals.

• a) IX (9): Predecessor = $\boxed{\text{VIII}}$, Successor = $\boxed{\text{X}}$
• b) XV (15): Predecessor = $\boxed{\text{XIV}}$, Successor = $\boxed{\text{XVI}}$
• c) XXIX (29): Predecessor = $\boxed{\text{XXVIII}}$, Successor = $\boxed{\text{XXX}}$
• d) XXXIV (34): Predecessor = $\boxed{\text{XXXIII}}$, Successor = $\boxed{\text{XXXV}}$
• e) XLVIII (48): Predecessor = $\boxed{\text{XLVII}}$, Successor = $\boxed{\text{XLIX}}$
• f) X (10): Predecessor = $\boxed{\text{IX}}$, Successor = $\boxed{\text{XI}}$
• g) XVI (16): Predecessor = $\boxed{\text{XV}}$, Successor = $\boxed{\text{XVII}}$
• h) XXX (30): Predecessor = $\boxed{\text{XXIX}}$, Successor = $\boxed{\text{XXXI}}$
• i) XL (40): Predecessor = $\boxed{\text{XXXIX}}$, Successor = $\boxed{\text{XLI}}$
• j) XIX (19): Predecessor = $\boxed{\text{XVIII}}$, Successor = $\boxed{\text{XX}}$

Q5: Compare the Roman numerals using $>$, $<$ or $=$.

• a) X $\boxed{\text{<}}$ XV
• b) XX $\boxed{\text{>}}$ XIX
• c) XL $\boxed{\text{<}}$ XLV
• d) XXV $\boxed{\text{=}}$ XXV
• e) IX $\boxed{\text{<}}$ XI
• f) XXXII $\boxed{\text{>}}$ XXVIII
• g) XLIX $\boxed{\text{<}}$ L
• h) XIV $\boxed{\text{<}}$ XVI