High School

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1. Write the following into Roman numerals:

(a) 59 = LIX
(b) 27 = XXVII
(c) 197 = CLXCVII
(d) 572 = DLXXII
(e) 675 = DCLXXV

2. Write in expanded form:

(a) 72876 = 70000 + 2000 + 800 + 70 + 6
(b) 98763 = 90000 + 8000 + 700 + 60 + 3
(c) 7654341 = 7000000 + 600000 + 50000 + 4000 + 300 + 40 + 1
(d) 8764321 = 8000000 + 700000 + 60000 + 4000

Answer :

Let's tackle the student's question step by step.

Part 1: Write the following numbers into Roman numerals

To convert Arabic numerals (our regular numbers) to Roman numerals, you need to know the basic symbols:

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

Now, let's convert the given numbers:

(a) 59 = LIX

  • L = 50
  • IX = 9 (which is 10 - 1)
  • Therefore, 59 in Roman numerals is LIX

(b) 27 = XXVII

  • XX = 20
  • V = 5
  • II = 2
  • Therefore, 27 in Roman numerals is XXVII

(c) 197 = CLXCVII (Note: There seems to be an error in the original question. The correct Roman numeral should be CXC VII, which is 197)

  • C = 100
  • XC = 90 (which is 100 - 10)
  • VII = 7
  • Therefore, 197 in Roman numerals is CXC VII

(d) 572 = DLXXII

  • D = 500
  • LXX = 70
  • II = 2
  • Therefore, 572 in Roman numerals is DLXXII

(e) 675 = DCLXXV

  • D = 500
  • CLX = 170
  • V = 5
  • Therefore, 675 in Roman numerals is DCLXXV

Part 2: Write the numbers in expanded form

Expanded form involves breaking down a number according to its place value. Let's do that for each number given:

(a) 72876 = 70000 + 2000 + 800 + 70 + 6

(b) 98763 = 90000 + 8000 + 700 + 60 + 3

(c) 7654341 = 7000000 + 600000 + 50000 + 4000 + 300 + 40 + 1

(d) 8764321 = 8000000 + 700000 + 60000 + 4000 (Note: The original doesn't fully expand; the correct should be 8000000 + 700000 + 60000 + 4000 + 300 + 20 + 1)

Understanding how to convert numbers into Roman numerals and expanded form can help you comprehend different ways numbers are represented. It enhances your grasp of place value and numeric systems, which is a fundamental aspect of mathematics.

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Rewritten by : Barada