How Accurate Are These Sig Fig Calculations and Unit Conversions?

  • Thread starter Thread starter cbrowne
  • Start date Start date
Click For Summary
SUMMARY

This discussion focuses on significant figure calculations and unit conversions, specifically addressing homework problems involving arithmetic operations and scientific notation. The calculations provided include operations such as subtraction, multiplication, and division, with results like 499.99 for 589.01−89.020 and 57.30 for 180.0/π. Unit conversions are also discussed, with examples such as converting 0.510 kg to grams resulting in 5.1 x 10² g. The importance of maintaining significant figures throughout calculations is emphasized, particularly in the context of scientific accuracy.

PREREQUISITES
  • Understanding of significant figures in mathematical operations
  • Familiarity with basic arithmetic operations (addition, subtraction, multiplication, division)
  • Knowledge of unit conversion techniques
  • Ability to express numbers in scientific notation
NEXT STEPS
  • Study the rules for significant figures in calculations
  • Practice unit conversions between metric and imperial systems
  • Learn about scientific notation and its applications in scientific calculations
  • Explore common pitfalls in significant figure calculations and how to avoid them
USEFUL FOR

Students in mathematics or science courses, educators teaching significant figures and unit conversions, and anyone needing to improve their accuracy in numerical calculations.

cbrowne
Messages
30
Reaction score
0
Hey I don't want to loose points for this primary question, could someone please go over my answers. Thanks!

Homework Statement




1. Perform the following operations and write your answers with appropriate
number of significant figures: (a) 589.01−89.020 (b) 1.0×9.00 (c) 180 /pi
(d) 180.0 /pi (e)3.901x10-5+ 1.0x10-7

2. Perform the following unit conversions and express the answer in scientific
notation: (a) 0.510 kg to g (b) 92 mi to km (c) 3 0.50 m to 3 cm (d) 15 μs to ms
(e) 60.0 km/h to m/s




The Attempt at a Solution



a) 589.01-89.020 = 499.99
b) 1.0 x 9.00 = 9.0
c) 180/ Π = 57
d) 180.0/Π = 57.30
e) 3.901 x 10^-5 + 1.0 x 10^-7 = 0.00004


2. a) 0.510kg x 1000g/1kg= 5.1 x 102g

b) 92 mi x 1.609344km/1mi= 1.48059 x 102 km

c) 0.50m3 x 1 000 000cm3/ 1m3 = 5 x 105 cm3

d) 15μs x 1ms/0.001 μs = 1.5 x 10-2ms

e) 60.0km/1hour = 65000m/3600 sec = 1.805556 x 101 m/s
 
Physics news on Phys.org
1e looks reeaall suspicious.

If I multiplied both numbers by 10^7 (for my convenience), I'd see 390.1 + 1.0

I don't have to convert it back to the proper decimal place to see there's a problem with saying 400