To convert the given expanded forms into numerals, we will follow a systematic approach for each part of the question.
### (i) Expanded Form:
`6 × 10^(4) + 3 × 10^(3) + 0 × 10^(2) + 7 × 10^(1) + 8 × 10^(0)`
**Step 1:** Calculate each term separately:
- \(6 × 10^4 = 6 × 10,000 = 60,000\)
- \(3 × 10^3 = 3 × 1,000 = 3,000\)
- \(0 × 10^2 = 0\)
- \(7 × 10^1 = 7 × 10 = 70\)
- \(8 × 10^0 = 8 × 1 = 8\)
**Step 2:** Add all the calculated values together:
- \(60,000 + 3,000 + 0 + 70 + 8\)
**Step 3:** Perform the addition:
- \(60,000 + 3,000 = 63,000\)
- \(63,000 + 0 = 63,000\)
- \(63,000 + 70 = 63,070\)
- \(63,070 + 8 = 63,078\)
**Final Answer:** The numeral is **63,078**.
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### (ii) Expanded Form:
`9 × 10^(6) + 7 × 10^(5) + 0 × 10^(4) + 3 × 10^(3) + 2 × 10^(2) + 9 × 10^(1) + 6 × 10^(0)`
**Step 1:** Calculate each term separately:
- \(9 × 10^6 = 9 × 1,000,000 = 9,000,000\)
- \(7 × 10^5 = 7 × 100,000 = 700,000\)
- \(0 × 10^4 = 0\)
- \(3 × 10^3 = 3 × 1,000 = 3,000\)
- \(2 × 10^2 = 2 × 100 = 200\)
- \(9 × 10^1 = 9 × 10 = 90\)
- \(6 × 10^0 = 6 × 1 = 6\)
**Step 2:** Add all the calculated values together:
- \(9,000,000 + 700,000 + 0 + 3,000 + 200 + 90 + 6\)
**Step 3:** Perform the addition:
- \(9,000,000 + 700,000 = 9,700,000\)
- \(9,700,000 + 0 = 9,700,000\)
- \(9,700,000 + 3,000 = 9,703,000\)
- \(9,703,000 + 200 = 9,703,200\)
- \(9,703,200 + 90 = 9,703,290\)
- \(9,703,290 + 6 = 9,703,296\)
**Final Answer:** The numeral is **9,703,296**.
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### (iii) Expanded Form:
`8 × 10^(5) + 6 × 10^(4) + 4 × 10^(3) + 2 × 10^(2) + 9 × 10^(1) + 6 × 10^(0)`
**Step 1:** Calculate each term separately:
- \(8 × 10^5 = 8 × 100,000 = 800,000\)
- \(6 × 10^4 = 6 × 10,000 = 60,000\)
- \(4 × 10^3 = 4 × 1,000 = 4,000\)
- \(2 × 10^2 = 2 × 100 = 200\)
- \(9 × 10^1 = 9 × 10 = 90\)
- \(6 × 10^0 = 6 × 1 = 6\)
**Step 2:** Add all the calculated values together:
- \(800,000 + 60,000 + 4,000 + 200 + 90 + 6\)
**Step 3:** Perform the addition:
- \(800,000 + 60,000 = 860,000\)
- \(860,000 + 4,000 = 864,000\)
- \(864,000 + 200 = 864,200\)
- \(864,200 + 90 = 864,290\)
- \(864,290 + 6 = 864,296\)
**Final Answer:** The numeral is **864,296**.
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