Why it happens: the division ends because 8 = 2 × 2 × 2 is built only from 2s, so an equivalent fraction over 1000 exists: 237/8 = (237 × 125)/1000 = 29625/1000 = 29.625. Three 2s in the denominator need three decimal places.
Q2.
Example 10: A shopkeeper has 9.5 kg of sugar and he wants to pack it equally in 4 bags. What is the weight of each bag of sugar?
Answer
Each bag weighs 2.375 kg.
9.5 ÷ 4
9 Ones ÷ 4 → 2 Ones each, 1 One remains
Regroup 1 One as 10 Tenths; with the 5 Tenths already there → 15 Tenths. Place the decimal point in the quotient.
15 Tenths ÷ 4 → 3 Tenths each, 3 Tenths remain
Regroup 3 Tenths as 30 Hundredths
30 Hundredths ÷ 4 → 7 Hundredths each, 2 Hundredths remain
Regroup 2 Hundredths as 20 Thousandths
20 Thousandths ÷ 4 → 5 Thousandths each, nothing remains
Each bag = 2.375 kg
Why it happens: a decimal dividend changes nothing about the method. The 5 Tenths of 9.5 simply join the 10 Tenths made by regrouping the leftover One, giving 15 Tenths to share. The point still goes in the quotient at the moment we move from Ones to Tenths.
Check it yourself: 2.375 × 4 = 9.5. ✓ Four bags of a little under 2.5 kg make a little under 10 kg.
Q3.
Example 11: What is the value of 0.06 ÷ 5?
Answer
0.06 ÷ 5 = 0.012
0.06 = 0 Ones + 0 Tenths + 6 Hundredths
0 Ones ÷ 5 → 0 Ones. Moving from Ones to Tenths, place the decimal point.
0 Tenths ÷ 5 → 0 Tenths
6 Hundredths ÷ 5 → 1 Hundredth each, 1 Hundredth remains
Regroup 1 Hundredth as 10 Thousandths
10 Thousandths ÷ 5 → 2 Thousandths
Quotient = 0.012
Why it happens: the zeros are not wasted steps — each one holds a place. Writing 0 in the Tenths place of the quotient is what keeps the 1 in the Hundredths place, where it belongs. Without it the answer would read 0.12, which is ten times too big.