Question

Convert the following to SI units:

a. $8.0in$ b.$66ft/s$

c. role="math" localid="1648656441116" $60mph$ d. role="math" localid="1648656467276" $14i{n}^2$

Short answer

a. $0.20m$ b. $20.12m/s$

c. $26.82m/s$ d.$9.0\times {10}^{-3}{m}^2$

Step-by-step solution

Part a Step 1: Introduction

The given digit $8.0in$should be converted into the unit $meter\left(m\right)$that is the SI unit of length.

Now,role="math" localid="1648657437480" $1in=2.54m$

Conversion of the given digit

The conversion of $in$to $meter$is,

$8in\times \left(\frac{2.54cm}{1in}\right)\times \left(\frac{{10}^{-2}m}{1cm}\right)=0.20m$

Part b Step 1: Introduction

The given digit should be converted from $ft/s$to $m/s$(SI unit of speed)

Now,$1ft=12in$and$1m=39.37in$

Conversion of the unit

The conversion of $ft/s$to $m/s$is,

$66ft/s=\frac{66ft}{1s}\times \frac{12in}{1ft}\times \frac{1m}{39.37in}=20.12m/s$

Part c Step 1: Introduction

The unit $mph$should be converted into $m/s.$

Now,$1mile=1.609km$

Conversion of unit

Converting the unit $mph$to $m/s$we get,

role="math" localid="1648659834859" $$\begin{gathered} 60mph=\left(\frac{60miles}{1hour}\right)\times \left(\frac{1.609km}{1mile}\right)\times \left(\frac{{10}^{3}m}{1km}\right)\times \left(\frac{1hour}{3600s}\right) \\ 60mph=26.82m/s \end{gathered}$$

Part d; Step 1: Introduction

The unit $inc{h}^2$should be converted into $m^2.$

Now,$1m=39.37inch$

Conversion of units

Converting the unit $i{n}^2$to $meter.$

$$\begin{gathered} 14i{n}^2=\left(14inc{h}^2\right)\times {\left(\frac{1m}{39.37inches}\right)}^2 \\ 14i{n}^2=9.0\times {10}^{-3}{m}^2 \end{gathered}$$