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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