Question 13 of 44intermediate🔍 AnalyzeShort Answer2 marks

Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?

Correct Answer

Yes, rows 1, 3, 7, and 9 have all digits from 0 to 9 appearing as ones digits.

Step 1: Check row 1 ones digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 — all digits present.

Step 2: Check row 3 ones digits: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 — all digits present.

Step 3: Check row 7 ones digits: 7, 4, 1, 8, 5, 2, 9, 6, 3, 0 — all digits present.

Step 4: Check row 9 ones digits: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 — all digits present.

Conclusion: Rows 1, 3, 7, and 9 have complete cycles because 1, 3, 7, and 9 are coprime to 10.

Exercise: Multiplication Chart | Q: 11 | (Page Page 9)
For More Understanding

Explanation

The chapter shows that rows 1, 3, 7, and 9 have all digits 0-9 appearing as ones digits. Row 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 (all digits). Row 3: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 (all digits). Row 7: 7, 4, 1, 8, 5, 2, 9, 6, 3, 0 (all digits). Row 9: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 (all digits). These rows have complete cycles because 1, 3, 7, and 9 are coprime to 10.

Solution Steps

  1. Step 1: Check row 1 ones digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 - all digits present

  2. Step 2: Check row 3 ones digits: 3, 6, 9, 2, 5, 8, 1, 4, 7, 0 - all digits present

  3. Step 3: Check row 7 ones digits: 7, 4, 1, 8, 5, 2, 9, 6, 3, 0 - all digits present

  4. Step 4: Check row 9 ones digits: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 - all digits present

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