Multiply 12.345 by 0.067 and round your answer to 4 decimal places.

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

12345 × 60 = 740700
12345 × 7 = 86415
12345 × 67 = 740700 + 86415 = 827115

Decimal places: 3 (in 12.345) + 3 (in 0.067) = 6
Product = 0.827115

To round to 4 places, look at the fifth digit: 1, below 5, so round down
0.827115 → 0.8271 → option (a)

Why the others are wrong

• (b)
  0.8764 — 0.8764 is above the ceiling 12.5 × 0.07 = 0.875. Both factors are smaller than 12.5 and 0.07, so the product must be below 0.875.
• (c)
  0.5687 — 0.5687 is below the floor 12 × 0.067 = 0.804. The product of 12.345 and 0.067 must be above 0.804, so this is far too small.
• (d)
  0.8765 — 0.8765 also exceeds the ceiling 0.875. Its closeness to 0.8764 invites a rounding choice between two values that are both wrong.

To multiply decimals, ignore the points, multiply the whole numbers, then count: the product has as many decimal places as the two factors together.

Rounding to n places looks only at the (n + 1)th digit. 5 or more rounds up, less than 5 leaves the nth digit as it is.

A floor and a ceiling, 12 × 0.067 = 0.804 and 12.5 × 0.07 = 0.875, leave 0.8271 as the one option between them.

Key facts

• Decimal places in a product = decimal places in the first factor + decimal places in the second.
• 12.345 × 0.067 = 0.827115 exactly.
• To round to 4 decimal places, check the 5th digit: 0 to 4 round down, 5 to 9 round up.

Common traps

• Counting the decimal places of one factor only: 827115 with 3 places is 827.115.
• Choosing between 0.8764 and 0.8765 on rounding grounds without checking that either is the product.

No directly related past PYQ was found.