Accepted answer
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Converting 52 inches in cm uses the exact international definition of the inch in centimeters, which makes the result precise.
Exact definition: \(1\ \text{inch} = 2.54\ \text{cm}\) (exact).
Therefore, converting inches to centimeters is a direct multiplication by \(2.54\).
Step-by-step method (inches to centimeters)
- Start with the length in inches, \(L_{\text{in}}\).
- Multiply by \(2.54\ \dfrac{\text{cm}}{\text{in}}\) so inches cancel and centimeters remain.
- Round only if the context requires it (the factor \(2.54\) is exact).
The conversion formula is:
\[ L_{\text{cm}} = L_{\text{in}} \times 2.54 \]Worked calculation: convert 52 inches to cm
Substitute \(L_{\text{in}} = 52\):
\[ L_{\text{cm}} = 52 \times 2.54 = 132.08\ \text{cm} \]The result is exact to the hundredth of a centimeter because the conversion factor is exact and the multiplication terminates.
Quick reference table (near 52 inches)
| Length (in) | Calculation | Length (cm) |
|---|---|---|
| 50 | \(50 \times 2.54\) | 127.00 |
| 51 | \(51 \times 2.54\) | 129.54 |
| 52 | \(52 \times 2.54\) | 132.08 |
| 53 | \(53 \times 2.54\) | 134.62 |
| 54 | \(54 \times 2.54\) | 137.16 |
Visualization: mapping 52 inches onto a centimeter scale
Common check
- Magnitude check: centimeters should be larger numerically because \(1\ \text{in}\) equals \(2.54\ \text{cm}\), so multiplying by \(2.54\) increases the number.
- Reverse check: dividing \(132.08\ \text{cm}\) by \(2.54\) returns \(52\ \text{in}\).
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