Question

Perform the calculation then

round to the appropriate number

of significant digits.

128.5 x 3.24

Answer 1

Answer: 416.34

Explanation:

128.5

⋅

3.24

Multiply using long multiplication.

128.5×3.24

To find the number of decimal places needed in the answer, add the number of decimal places in the multiplier and multiplicand. In this case, there is a total of

3

, so the answer must have

3

decimal places as well.

416.34

Answer 2

416 (3 s.f.)

Explanation:

To multiply decimals, begin by multiplying the numbers as if there is no decimal:

`\large\begin{array}{cccccc}&& 1 & 2 & 8 & 5\\* && & 3 &2 & 4\\\cline{1-6} && 5 & 1 & 4 & 0\\&2&5&7&0&0\\3&8&5&5&0&0\\\cline{1-6}4&1&6&3&4&0\\\cline{1-6}^1&^1&^1&&\phantom{^{(1)/(2)}}&\end{array}`

Count the number of digits after the decimal point in each factor:

• 128.5 → 1 digit after the decimal point.
• 3.24 → 2 digits after the decimal point.

Therefore, there is a total of 3 digits after the decimal points.

Put the same number of digits after the decimal point in the product.

Therefore, the solution is to the multiplication is:

• 416.340

The factor with the fewest signification figures is 3.24.

This number has 3 significant figures.

Therefore, the solution to 3 significant figures is:

• 416 (3 s.f.)