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NIST SP 811 factor-label chains: 60 mi/h to m/s, 14.7 psi to kPa, 1 Btu to J, with the rounding reasoning of Appendix B.7.2

Tool	Units and Sig Figs Tutor
Source	Thompson, A., and Taylor, B. N. (2008). Guide for the Use of the International System of Units (SI). NIST Special Publication 811, National Institute of Standards and Technology, Gaithersburg, MD. Appendix B.3 (use of the factors, 11.8 atm = 1.20 MPa), B.7.1 (rounding rules), B.7.2 (36 ft = 10.9728 m reported as 11.0 m), B.8 (factors).
Level	Undergraduate

Problem

Write the chain of conversion factors, as a textbook does, that turns 60 mi/h into m/s, 14.7 psi into kPa and 1 Btu into J; mark each factor exact or rounded with its source; cancel the units factor by factor; and round each result to the significant figures the input warrants, comparing the classroom rule (same count as the input) with the relative-rounding-error reasoning of SP 811 B.7.2.

Inputs to Enter

Part: factor-label conversion; chain: textbook definitions (1 mi = 5280 ft, 1 ft = 12 in, 1 in = 2.54 cm, 1 h = 60 min, 1 min = 60 s; 1 psi = 1 lbf/in², 1 lbf = 4.448 221 615 260 5 N, 1 Pa = 1 N/m²; 1 Btu IT = 1055.055 852 62 J)
Lines: 60 mi/h -> m/s ; 14.7 psi -> kPa ; 1 Btu -> J ; rounding rule: round half to even (ASTM E29); Every step on

Open the Units and Sig Figs Tutor tool (loaded with this example)

Answers

60 mi/h × (5280 ft/1 mi)(12 in/1 ft)(2.54 cm/1 in)(1 m/100 cm)(1 h/60 min)(1 min/60 s) = 26.8224 m/s; the product of the six exact factors is 0.44704 m/s per mi/h (SP 811 B.8: mi/h → m/s 4.4704 E−01 exact); 60 has one significant figure (trailing zero ambiguous, SP 811 §7.9): 3 × 10¹ m/s; written 60. it gives 27 m/s, and the SP 811 B.7.2 reading is 26.8 m/s
14.7 psi × (1 lbf/in² / 1 psi)(4.448 221 615 N/1 lbf)(1 in/2.54 cm)²(100 cm/1 m)²(1 Pa / 1 N/m²)(1 kPa/1000 Pa) = 101.3529 kPa (SP 811 B.8: psi → kPa 6.894 757); classroom rule 101 kPa (three significant figures, relative rounding error ±0.5 %), SP 811 B.7.2 reading 101.4 kPa (the input's ±0.34 % is finer than 101's ±0.5 %)
1 Btu × (1055.055 852 62 J / 1 Btu) = 1055.056 J (SP 811 B.8 prints 1.055 056 E+03); one significant figure: 1 × 10³ J; as an exact quantity 1055.06 J
SP 811's own examples reproduced in the test: 36 ft × 0.3048 m/ft = 10.9728 m, classroom 11 m, B.7.2 11.0 m (RE of 36 is ±1.4 %, of 11 ±4.5 %, of 11.0 ±0.45 %); 11.8 atm × 101 325 Pa/atm = 1 195 635 Pa = 1.20 MPa

Notes

The tool's default inputs are these three lines; press Submit. The significant-figures part reproduces the OpenStax Chemistry 2e §1.5 examples (1.0023 g + 4.383 g = 5.385 g, 486 g − 421.23 g = 65 g, 0.6238 cm × 6.6 cm = 4.1 cm², 421.23 g / 486 mL = 0.867 g/mL), Zumdahl's 1.23 × 4.5 = 5.5 and 12.11 + 18.0 + 1.013 = 31.1, the SP 811 B.7.1 rounding examples (6.974 951 5 → 6.97, 7.0, 6.9750, 6.974 952; 6.974 950 5 → 6.974 950) and the ASTM E29-67 §3.5 / §3.6 / Table 1 cases (89,490 → 89,000 psi; 6025 → 6000 and 6075 → 6100 to the nearest 50; 59,950 → 60,000; 56.5 → 56); every value is checked in test_sig_figs_tutor.php (413 checks) and the rounding modes against Python's decimal module (References/Units-SigFigs/rounding_decimal_check.py).