Question

1. how many gm are in 1.50 x 10² mm?

Explanation:

Step1: Recall unit conversions

We know that \(1\space Gm = 10^{9}\space m\) and \(1\space Mm=10^{6}\space m\). So we can convert \(Mm\) to \(Gm\) by using the conversion factor.
First, let's express the given quantity in meters. The given quantity is \(1.50\times 10^{2}\space Mm\). Since \(1\space Mm = 10^{6}\space m\), we have:
\(1.50\times 10^{2}\space Mm\times10^{6}\frac{m}{Mm}=1.50\times 10^{2 + 6}\space m=1.50\times 10^{8}\space m\)

Step2: Convert meters to Gm

Now we convert meters to gigameters. Since \(1\space Gm=10^{9}\space m\), we divide the number of meters by \(10^{9}\) to get gigameters:
\(\frac{1.50\times 10^{8}\space m}{10^{9}\frac{m}{Gm}}=1.50\times 10^{8-9}\space Gm = 1.50\times 10^{- 1}\space Gm=0.15\space Gm\)

Alternatively, we can use the direct conversion between \(Mm\) and \(Gm\). Since \(1\space Gm = 10^{3}\space Mm\) (because \(10^{9}\space m=10^{3}\times10^{6}\space m = 10^{3}\space Mm\)), so the conversion factor from \(Mm\) to \(Gm\) is \(\frac{1\space Gm}{10^{3}\space Mm}\)

Then, \(1.50\times 10^{2}\space Mm\times\frac{1\space Gm}{10^{3}\space Mm}=\frac{1.50\times 10^{2}}{10^{3}}\space Gm=1.50\times 10^{2 - 3}\space Gm=1.50\times 10^{-1}\space Gm = 0.15\space Gm\)

Answer:

\(0.15\space Gm\) (or \(1.50\times 10^{- 1}\space Gm\))