Question

what is the weight in newtons of an object that has a mass of 610 mg? express your answer in newtons using three significant figures.

Explanation:

Step1: Convert mass unit to kg

We know that \(1\space Mg = 10^{6}\space g\) and \(1\space kg=10^{3}\space g\), so \(1\space Mg = 10^{3}\space kg\). Then for \(610\space Mg\), the mass \(m\) in kg is \(m = 610\times10^{3}\space kg=6.10\times 10^{5}\space kg\) (we keep three significant figures here as required in the final answer).

Step2: Use weight formula \(W = mg\)

The formula for weight \(W\) is \(W=mg\), where \(g = 9.81\space m/s^{2}\) (acceleration due to gravity). Substitute \(m = 6.10\times 10^{5}\space kg\) and \(g=9.81\space m/s^{2}\) into the formula:
\(W=(6.10\times 10^{5}\space kg)\times(9.81\space m/s^{2})\)
\(W = 6.10\times9.81\times 10^{5}\space N\)
Calculate \(6.10\times9.81 = 59.841\), so \(W=59.841\times 10^{5}\space N = 5.9841\times 10^{6}\space N\)

Step3: Round to three significant figures

Rounding \(5.9841\times 10^{6}\space N\) to three significant figures gives \(5.98\times 10^{6}\space N\) (or \(5.98\times10^{6}\) can also be written as \(5980000\) but in scientific notation with three significant figures it is \(5.98\times 10^{6}\)).

Answer:

\(5.98\times 10^{6}\space N\) (or \(5980000\space N\) but in three - significant - figure scientific notation it is \(5.98\times 10^{6}\space N\))