Uploaded May 2016 | Updated September 2026, 2 hours ago
Video about why you shouldn't round numbers too much or too early, and loss of significance during the calculation process.
Problem taken from "Numerical Mathematics and Computing (7th Edition)" by W. Cheney and D. Kincaid. The book uses a different method of solving the equations, and uses example to show importance of keeping any intermediate answers in full when doing calculations with a computer.
If you're lazy to watch the video, we're basically going to solve the simultaneous equations;
0.1036x + 0.2122y = 0.7381, and
0.2081x + 0.4247y = 0.9327.
Keeping all numbers in calculations to 2 significant figures, we get solution x = -27 and y = 17.
Keeping all numbers in calculations to 4 significant figures, we get solution x = -680.4 and y = 335.6.
Keeping all numbers in calculations to 10 significant figures, we get solution x = -722.6524540 and y = 356.2907364.
Using a calculator, we get solution x = -722.6524703 and y = 356.2907442.
Four different pairs of answers.
Video about why you shouldn't round numbers too much or too early, and loss of significance during the calculation process.
Problem taken from "Numerical Mathematics and Computing (7th Edition)" by W. Cheney and D. Kincaid. The book uses a different method of solving the equations, and uses example to show importance of keeping any intermediate answers in full when doing calculations with a computer.
If you're lazy to watch the video, we're basically going to solve the simultaneous equations;
0.1036x + 0.2122y = 0.7381, and
0.2081x + 0.4247y = 0.9327.
Keeping all numbers in calculations to 2 significant figures, we get solution x = -27 and y = 17.
Keeping all numbers in calculations to 4 significant figures, we get solution x = -680.4 and y = 335.6.
Keeping all numbers in calculations to 10 significant figures, we get solution x = -722.6524540 and y = 356.2907364.
Using a calculator, we get solution x = -722.6524703 and y = 356.2907442.
Four different pairs of answers.
