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Write the numeral whose expanded form is...

Write the numeral whose expanded form is given below:
( i ) `6 xx 10^(4)+3 xx 10^(3)+0 xx 10^(2)+7 xx 10^(1)+8 xx 10^(0)`
( ii ) `9 xx 10^(6)+7 xx 10^(5)+0 xx 10^(4)+3 xx 10^(3)+2 xx 10^(2)+9 xx 10^(1)+6 xx 10^(0)`
( iii ) `8 xx 10^(5)+6 xx 10^(4)+4 xx 10^(3)+2 xx 10^(2)+9 xx 10^(1)+6 xx 10^(0)`

Text Solution

AI Generated Solution

The correct Answer is:
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**. --- ### (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**. --- ### (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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