Why it happens: the product of the two fractions has a denominator made only of tens. If the product of the numerators is a multiple of that denominator, the fraction reduces to a whole number. In 2.5 × 0.4 the numerators give 25 × 4 = 100, and the denominator is also 100, so the answer is exactly 1.
Tip: pair a decimal ending in 5 or 25 with one ending in 2, 4 or 8. Those pairs often finish on a whole number, because 5 × 2 = 10.
Q2.
Math Talk: Can the product of a decimal and a natural number be a natural number?
Why it happens: multiplying only changes the numerator. So the answer is a whole number whenever the natural number cancels the denominator. 0.25 has denominator 100, and 8 × 25 = 200, which 100 divides exactly.
Did you know? This is why shopkeepers like quarters. Four items at ₹0.25 come to exactly ₹1 — no paisa left over.
Q3.
Example 3: The distance between Ajay's school and his home is 827 m. He walks to school in the morning and then walks back home in the evening, 6 days a week. How much does he walk in a week? Answer in kilometres.
Answer
Ajay walks 9.924 km in a week.
First put the distance in kilometres. 827 m = 827/1000 km = 0.827 km.
In one day (to school and back):
0.827 × 2 = 827/1000 × 2 = 1654/1000 = 1.654 km
In a week (6 days):
1.654 × 6 = 1654/1000 × 6 = 9924/1000 = 9.924 km
Why it happens: multiplying by 2 and then by 6 only touches the numerator, because 2 and 6 are whole numbers. The denominator stays 1000 throughout, so the answer keeps exactly three digits after the point.
Check it yourself: 827 × 12 = 9924 metres in a week, and 9924 m = 9.924 km. Same answer, reached the other way round.
Q4.
Example 4: Find the area of the given rectangle. (Length 13.3 cm, breadth 5.7 cm)
The rectangle from page 70. Multiply the two counting numbers first, then place the point.
Why it happens: 57 × 133 = 7581 is an ordinary multiplication. Dividing by 10 twice — once for each factor — is the same as dividing by 100, which slides the point two places left: 7581 → 75.81.
Q5.
Observe the number of digits after the decimal point in the multiplier, the multiplicand and the product. Also note the number of zeroes in the denominator. (Table: 9.5 × 5, 12.5 × 7.5, 1.64 × 6, 5.7 × 13.35)
Answer
In every row, the decimal places in the product are the sum of the decimal places in the two numbers.
Example
As fractions
Multiplier
Multiplicand
Product
Zeroes in denominator
9.5 × 5 = 47.5
95/10 × 5/1 = 475/10
1
0
1
1
12.5 × 7.5 = 93.75
125/10 × 75/10 = 9375/100
1
1
2
2
1.64 × 6 = 9.84
164/100 × 6/1 = 984/100
2
0
2
2
5.7 × 13.35 = 76.095
57/10 × 1335/100 = 76095/1000
1
2
3
3
Why it happens: a number with 1 decimal place is a fraction over 10, one with 2 decimal places is over 100. Multiplying the fractions multiplies the denominators, so 10 × 100 = 1000 — the zeroes simply add up. And the number of zeroes in the denominator is the number of digits after the point. That is the whole reason the decimal places add.
Tip: a whole number like 5 or 6 counts as 0 decimal places, because 5 = 5/1 and 1 has no zeroes at all.