Lesson 0.1 - REVIEW Significant Digits
MATH REVIEW: SIGNIFICANT DIGITS
VIDEO (29:06 min)
https://www.youtube.com/watch?v=EjFlnpewsHwVideo is not accessible in some countries. If you cannot view it, you might need VPN to do so.
PHYSICS AS AN EMPIRICAL SCIENCE
- Physics is based on a correspondence between measurements and theory.
- Let's think about measurements for a moment.
- All measurements have an inherent uncertainty defined as the measuring device.
- Example: A standard ruler may measure something as being 13.2 cm however there is an uncertainty of \( \pm \) 0.1 cm.
- We need a way to deal with these uncertainties in our calculations.
SIGNIFICANT DIGITS / FIGURES (Sig. figs.)
The following digits are significant:
- All non-zero digits
- All zeros between non-zeros
- E.g. 102.05 has 5 sig. figs.
- All zeros left of an understood decimal and right of a non-zero digit
- E.g. 405 000. has 6 sig. figs.
- All zeros to the right of a decimal point and right of a non-zero digit
- E.g. 0.8050 and 50.00 have 4 sig. figs.
The following digits are not significant:
- All zeros to the right of a decimal point but to the left of a non-zero digit
- E.g. 0.000403 has 3 sig. figs.
CONSTANTS and EXACT NUMBERS
- Significant digits only matter in measurements
- Constants taken from literature and exact numbers have an infinite number of significant digits
- Ex. \( g=9.81 m/s^2 \) and the 2 in the equation \( \Delta t= \sqrt[]{ \frac{2 \Delta d }{g} } \)
OPERAIONS with SIG. DIGS.
- Addition and subtraction: round answer to the least number of digits after the decimal as were provided in the original measurement.
- Multiplication and Division: answer should have the same number of sig. figs. as the measurement with the fewest sig. figs.
SCIENTIFIC NOTATION
Scientific notation is a convenient way of writing numbers of any magnitude and expressing their accuracy by using only sig. figs.
Examples:
- Radius of a hydrogen atom = 0.000 000 000 053 m =
- Radius of Earth = 6 380 000 m = \( 6.38 \times10^6 \) m
Sửa lần cuối: Thứ bảy, 26 Tháng 4 2025, 2:59 PM