Answer
\[ 46\ \text{in} = 46 \times 2.54\ \text{cm} = 116.84\ \text{cm}. \]
Conversion factor (exact definition)
The inch is defined exactly in terms of centimeters: \[ 1\ \text{in} = 2.54\ \text{cm}. \] This exact conversion factor makes inch-to-centimeter conversions precise.
Step-by-step: 46 inches to cm
Step 1: Set up unit cancellation (dimensional analysis).
\[ 46\ \text{in}\times\frac{2.54\ \text{cm}}{1\ \text{in}} \] The unit “in” cancels, leaving centimeters.
Step 2: Multiply the numbers.
\[ 46 \times 2.54 = (46 \times 2) + (46 \times 0.5) + (46 \times 0.04) \] \[ = 92 + 23 + 1.84 = 116.84. \]
Step 3: Attach the correct unit.
\[ 46\ \text{in} = 116.84\ \text{cm}. \]
Quick reference table
| Quantity | Value |
|---|---|
| Given | \(46\ \text{in}\) |
| Conversion factor | \(1\ \text{in} = 2.54\ \text{cm}\) |
| Exact computation | \(46 \times 2.54 = 116.84\) |
| Result | \(116.84\ \text{cm}\) |
Visualization: 46 inches on an inches-to-cm scale
Scale view: 0–50 inches mapped to centimeters