Question

Convert the following to SI units:

a. $75in$ b. $3.45\times {10}^{6}yr$

c. $62ft/day$ d. $2.2\times {10}^{4}m{i}^2$

Short answer

a. $75inch=1.91m$

b. $3.45\times {10}^{6}yr=1.09\times {10}^{14}s$

c. $62ft/day=2.2\times {10}^{-4}m/s$

d.$2.2\times {10}^{4}m{i}^2=5.7\times {10}^{10}{m}^2$

Step-by-step solution

Part a; Step 1: Introduction

The unit $inch$should be converted into $meter$(SI unit of distance/length)

Conversion of the unit

The given digits should be converted as,

$$\begin{gathered} 75inch=75inch\times \left(\frac{2.54cm}{1inch}\right)\times \left(\frac{{10}^{-2}m}{1cm}\right) \\ 75inch=1.91m \end{gathered}$$

Part b Step 1: Introduction

The unit $year$ should be converted into $second$ (SI unit of time)

Conversion of unit

The given digits should be converted as,

$$\begin{gathered} 3.45\times {10}^{6}yr=3.45\times {10}^{6}yr\left(\frac{365days}{1yr}\right)\left(\frac{24h}{1day}\right) \\ \times \left(\frac{60m}{1h}\right)\left(\frac{60s}{1m}\right) \\ 3.45\times {10}^{6}yr=1.09\times {10}^{14}s \end{gathered}$$

Part c; Introduction

The unit $ft/day$is a unit of speed, should be converted into SI unit of the same as$m/s$.

Conversion of the unit

The given digits should be converted in SI unit as,

$$\begin{gathered} 62ft/day=\left(\frac{62ft}{1day}\right)\left(\frac{1mile}{5280ft}\right)\left(\frac{1.609km}{1mile}\right)\left(\frac{{10}^{3}m}{1km}\right) \\ \times \left(\frac{1day}{24h}\right)\left(\frac{1h}{3600s}\right) \\ 62ft/day=2.2\times {10}^{-4}m/s \end{gathered}$$

Part d; Step 1: Introduction

The unit $m{i}^2$is a unit of area that should be converted into$m^2\left(SI\right).$

Conversion of unit

The given digits should be converted in SI unit as,

$$\begin{gathered} 2.2\times {10}^{4}m{i}^2=2.2\times {10}^{4}m{i}^2{\left(\frac{5280ft}{1mi}\right)}^2{\left(\frac{12in}{1ft}\right)}^2 \\ \times {\left(\frac{1m}{39.37in}\right)}^2 \\ 2.2\times {10}^{4}m{i}^2=5.7\times {10}^{10}{m}^2 \end{gathered}$$