Accepted answer
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Converting cm to inches uses the exact definition of the inch in centimeters, which makes the conversion precise and consistent in science and engineering.
Exact definition: \(1\ \text{inch} = 2.54\ \text{cm}\) (exact).
Therefore, \(1\ \text{cm} = \dfrac{1}{2.54}\ \text{inches} \approx 0.3937008\ \text{in}\).
Step-by-step method (centimeters to inches)
- Start with the length in centimeters, \(L_{\text{cm}}\).
- Divide by \(2.54\ \dfrac{\text{cm}}{\text{inch}}\) so that centimeters cancel and inches remain.
- Round to the required precision (construction often uses fractions; lab work often uses decimals).
The conversion formula is:
\[ L_{\text{in}} = \frac{L_{\text{cm}}}{2.54} \]Worked example: convert 25 cm to inches
Take \(L_{\text{cm}} = 25\ \text{cm}\). Apply the formula:
\[ L_{\text{in}} = \frac{25}{2.54} \approx 9.842519685\ \text{in} \]Rounded to four decimal places: \(9.8425\ \text{in}\). Rounded to two decimal places: \(9.84\ \text{in}\).
Quick reference table
| Length (cm) | Length (inches) | Rounded (2 d.p.) |
|---|---|---|
| 1 | \(\dfrac{1}{2.54} \approx 0.3937008\) | 0.39 |
| 2.54 | \(\dfrac{2.54}{2.54} = 1\) | 1.00 |
| 10 | \(\dfrac{10}{2.54} \approx 3.9370079\) | 3.94 |
| 25 | \(\dfrac{25}{2.54} \approx 9.8425197\) | 9.84 |
| 30 | \(\dfrac{30}{2.54} \approx 11.8110236\) | 11.81 |
Visualization: a simple ruler-style mapping (cm to inches)
Common checks and rounding guidance
- Direction check: inches should be smaller than centimeters numerically because \(1\ \text{in} = 2.54\ \text{cm}\) is longer than \(1\ \text{cm}\).
- Exact vs approximate: \(2.54\) is exact; any rounding occurs only after division.
- Typical rounding: for most practical uses, 2 decimal places is sufficient; for machining, use more decimals as required by tolerances.
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