Physics and Math Chapter 10 & 11: Mathematics and Reasoning about Design and Execution Flashcards
Scientific notation
[significand] x 10^[Exponent]
Significand must be:
greater than or equal to 1 and less than 10
The exponent in scientific notation must be
an integer
Significant figures
include all nonzero digits and any trailing zeroes in a number with a decimal point
Sig figs in addition and subtraction
reduce the answer to have the same number of decimal places as the number with the fewest decimal places
Sig figs in multiplication and division
reduce the answer to have the same number of sig figs as the number with the fewest number of sig figs
Tips for estimating in multiplication and division
In multiplication, if one number is rounded up, the other should be rounded down in proportion.
In division, if one number is rounded up, the other should also be rounded up.
Exponents
A notation for repeated multiplication. They may be manipulated mathematically, especially when the bases are the same.
Logarithms
the inverse of exponents and are subject to similar mathematical manipulations.
Natural logarithms
use base e
Direct relationships
as one variable increases, the other increases in proportion
Inverse relationships
as one variable increases, the other decreases in proportion
Conversions between metric prefixes require:
multiplication by corresponding powers of 10.
Scientific method:
a series of 8 steps for the generation of new knowledge
- generate a testable hypothesis
- gather data and resources
- form a hypothesis
- collect new data
- analyze the data
- interpret the data and existing hypothesis
- publish
- verify results
FINER method
assesses the value of a research question on the basis of whether or not it is feasible, interesting, novel, ethical and relevant.