Question 15 of 44intermediate🔍 AnalyzeShort Answer2 marks

Is there a row in which 0 appears as the ones digit only once? Which rows have this property?

Correct Answer

Yes, rows 1, 3, 7, and 9 have 0 appearing as the ones digit only once.

Row 1: 0 appears only in 1×101 \times 10 = 10

Row 3: 0 appears only in 3×103 \times 10 = 30

Row 7: 0 appears only in 7×107 \times 10 = 70

Row 9: 0 appears only in 9×109 \times 10 = 90

∴ In these rows, all digits 0-9 appear exactly once as ones digits, so 0 appears only once (at position 10).

Exercise: Multiplication Chart | Q: 13 | (Page Page 9)
For More Understanding

Explanation

The chapter shows that in rows 1, 3, 7, and 9, all digits 0-9 appear exactly once as ones digits. This means 0 appears only once - at position 10 (when the row number is multiplied by 10). For example, row 1: 1×101 \times 10=10 (ones digit 0 appears once). Row 3: 3×103 \times 10=30 (ones digit 0 appears once). These rows have complete cycles of ones digits.

Solution Steps

  1. Step 1: In row 1, 0 appears only in 1×101 \times 10=10

  2. Step 2: In row 3, 0 appears only in 3×103 \times 10=30

  3. Step 3: In row 7, 0 appears only in 7×107 \times 10=70

  4. Step 4: In row 9, 0 appears only in 9×109 \times 10=90

  5. Step 5: These rows have all digits 0-9 appearing exactly once

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