Can you find the quotients of , and ?

Question

Homi · Accepted Answer

We will use long division to find the decimal quotients.

Step 1 — Dividing 10 by 9

We want to divide 10 by 9. Let us use the long division method. We will find the quotient as a decimal. First, divide 10 by 9. The quotient is 1. The remainder is 1. $10 \div 9 = 1 \text{ with remainder } 1$ Now, we add a decimal point. We add a zero to the remainder. The new number is 10. Divide 10 by 9 again. The quotient is 1. The remainder is 1. This pattern will repeat forever. So, the quotient is a repeating decimal. $10 \div 9 = 1.111...$

$\boxed{1.\overline{1}}$

Diagram 1

Step 2 — Dividing 100 by 11

Now we divide 100 by 11. We use the long division method again. First, divide 100 by 11. We know that $11 \times 9 = 99$ . The quotient is 9. The remainder is 1. $100 \div 11 = 9 \text{ with remainder } 1$ We add a decimal point. We add a zero to the remainder. The new number is 10. Divide 10 by 11. 11 goes into 10 zero times. The quotient digit is 0. The remainder is 10. We add another zero. The new number is 100. Divide 100 by 11. The quotient digit is 9. The remainder is 1. This pattern will repeat. The digits 09 will repeat. So, the quotient is a repeating decimal. $100 \div 11 = 9.0909...$

$\boxed{9.\overline{09}}$

Diagram 2

Answer

(i) The quotient of $10 \div 9$ is $\mathbf{1.\overline{1}}$ . (ii) The quotient of $100 \div 11$ is $\mathbf{9.\overline{09}}$ .

Question 13

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