Multiply 0.45 by 0.6 and express the result as a decimal.

Correct — B. Multiply as whole numbers, then place the decimal point.

Drop the points: 45 × 6 = 270
Count decimal places: 2 (in 0.45) + 1 (in 0.6) = 3
Place the point three digits from the right: 0.270
Drop the trailing zero: 0.27 → option (b)

Why the others are wrong

• (a)
  0.86 — 0.86 is larger than both factors. Multiplying 0.45 by 0.6, a number below 1, must give less than 0.45.
• (c)
  0.76 — 0.76 also exceeds 0.45, so it cannot be 0.45 × 0.6. A factor below 1 shrinks the other factor: 0.6 of 0.45 is 0.27.
• (d)
  0.54 — 0.54 is 2 × 0.27, double the true product. It also exceeds 0.45, which a product with a factor below 1 cannot do.

Decimal places add under multiplication. A factor with 2 places times a factor with 1 place gives 3 places, because 0.45 = 45⁄100 and 0.6 = 6⁄10, and 100 × 10 = 1000.

A quick sense check: multiplying by a number between 0 and 1 makes the result smaller than the other factor, so 0.45 × 0.6 must be below 0.45.

Key facts

• Decimal places in a product = the sum of the decimal places in its factors.
• 0.45 × 0.6 = 270⁄1000 = 0.27.
• Multiplying by a number between 0 and 1 gives a smaller result.

Common traps

• Counting the decimal places of one factor only: two places turns 270 into 2.70, ten times too big.
• Discarding the zero of 270 before placing the point: 27 with three places gives 0.027, ten times too small.

No directly related past PYQ was found.