How many digits appear to the right of the decimal point in the product 95.75 × 0.02554?

Problem restatementDetermine the number of decimal places in the product of two terminating decimals.

Given data

• 95.75 has 2 decimal places.
• 0.02554 has 5 decimal places.

Concept/ApproachThe product of two terminating decimals has, before simplification, a number of decimal places equal to the sum of the decimal places of the factors. Any common factors of 2 or 5 between numerator and denominator can reduce trailing zeros, but here the net decimal places remain 7.

Step-by-Step calculation2 + 5 = 7 decimal places

Verification/AlternativeWrite 95.75 = 3829/40 and 0.02554 = 2554/100000. Product = (3829 × 2554) / 4,000,000. After canceling a single factor of 2 with the even numerator 2554, the denominator still has 2⁷5⁶, so the equivalent denominator 10⁷ yields 7 decimal places.

Common pitfallsForgetting that cancellation only reduces trailing zeros, not the total internal precision logic; in this case, cancellation preserves 7 places.

Final Answer7