Question

converting length with two conversion factors
units of length
customary system units\tmetric system units
1 inch\t2.54 centimeters
1 foot\t0.3048 meters
1 mile\t1.61 kilometers
how many inches are in 4 meters?
meters → feet → inches
$4\text{m} \times \frac{a}{b} \times \frac{c}{d} \times \frac{1}{1} = 157.48\text{in}$
(the chart shows the conversion between customary system units (1 inch, 1 foot, 1 mile) and metric system units (2.54 centimeters, 0.3048 meters, 1.61 kilometers) for length. then there is a calculation process to find how many inches are in 4 meters, with placeholders a, b, c, d for the conversion factors.)

Explanation:

Step1: Identify meter to foot factor

We know $1 \text{ foot} = 0.3048 \text{ meters}$, so the conversion factor from meters to feet is $\frac{1 \text{ foot}}{0.3048 \text{ meters}}$. Here, $a=1 \text{ foot}$, $b=0.3048 \text{ meters}$.

Step2: Identify foot to inch factor

We know $1 \text{ foot} = 12 \text{ inches}$, so the conversion factor from feet to inches is $\frac{12 \text{ inches}}{1 \text{ foot}}$. Here, $c=12 \text{ inches}$, $d=1 \text{ foot}$.

Step3: Set up conversion equation

$$4 \text{ m} \times \frac{1 \text{ foot}}{0.3048 \text{ m}} \times \frac{12 \text{ inches}}{1 \text{ foot}}$$

Step4: Calculate the result

First, cancel units: meters and feet cancel out, leaving inches.
$$4 \times \frac{1}{0.3048} \times 12 \text{ inches} \approx 4 \times 3.2808 \times 12 \text{ inches} \approx 157.48 \text{ inches}$$

Answer:

$a=1 \text{ foot}$, $b=0.3048 \text{ meters}$, $c=12 \text{ inches}$, $d=1 \text{ foot}$
Final length: $\approx 157.48$ inches