Question

what is the weight in newtons of an object that has a mass of 0.10 mg? express your answer in newtons using three significant figures.

Explanation:

Step1: Recall the formula for weight

Weight \( W \) is given by the formula \( W = m \times g \), where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

Step2: Convert mass to kilograms

The mass \( m = 0.10 \, \text{mg} \). We know that \( 1 \, \text{mg} = 10^{-6} \, \text{kg} \), so \( 0.10 \, \text{mg} = 0.10 \times 10^{-6} \, \text{kg} = 1.0 \times 10^{-7} \, \text{kg} \).

Step3: Calculate the weight

Substitute \( m = 1.0 \times 10^{-7} \, \text{kg} \) and \( g = 9.81 \, \text{m/s}^2 \) into the weight formula:
\( W = (1.0 \times 10^{-7} \, \text{kg}) \times (9.81 \, \text{m/s}^2) \)
\( W = 9.81 \times 10^{-7} \, \text{N} \)
Rounding to three significant figures, we get \( W = 9.81 \times 10^{-7} \, \text{N} \) (or \( 0.981 \times 10^{-6} \, \text{N} \), but in scientific notation with three significant figures, it's \( 9.81 \times 10^{-7} \, \text{N} \)).

Answer:

\( 9.81 \times 10^{-7} \)