Week 1 Flashcards
What is accuracy in measurement?
What is precision in measurement?
What are significant digits?
The number of digits in a measurement or result indicates how accurate the number is.
27 has 2 SD
27.3 has 3 SD and implies more accuracy
When are trailing digits significant or insignificant?
Trailing zeros AFTER THE DECIMAL are significant if stated
Trailing zeros are not significant if there is no decimal point in the quoted number
Are leading zeros significant?
No. It doesn’t matter if they are before or after the decimal
0.0045 has 2 SD
1.0045 has 5 SD
What are significant digits?
Numbers with meaning
What is the convention for✖️ or➗
The result has the same number of significant digits as the LEAST accurate number used in the calculation
E.g 3.0 x 4.3574 the result will be rounded to 2 SD therefore it’ll be 13
What is precision?
The smallest order of tens. More numbers after the decimal. Think of it as fineness of a measurement
Which is precise which is accurate 7.123 and 17.1
Precise: 7.123
Accurate: 17.1
What is the convention for ➕ or ➖
When adding or subtracting numbers, the result has the same precision as the LEAST precise number used in the calculation.
E.g 57 + 0.045 = 57
As 57 is the least precise therefore 2SD is used and it’s rounded to the nearest full number
What is margin of error?
One half of the size of the last significant place
E.g measurement of 45kg is precise to the nearest 1kg
Margin of error is half of 1kg or 0.5kg
Margin of error acknowledges that rounding has occurred due to the limit of our measuring device
Why do significant digits matter?
As numerical values are information they must be communicated clearly
When we express clinical data with more digits than the values used in producing that data, we mislead the recipient regarding the level of accuracy
What is scientific notion?
An efficient method of representing numbers that have wide range of magnitude (sizes)
Expresses the value as a number between 1 and 10 that is multipled by 10 to some exponent
751 is expressed as 7.51 x 102(2 is a power)
0.00031 is expressed as 3.1 x 10-4 -4 is a power)
Conventions for Scientific Notation
It’s based on ‘a x 10 to the power of b’
a is the number between 1-10
B expresses the order of magnitudes (how many times 10 is multiplied by itself)
What communicates accuracy of a number?
The number of digits after the decimal place
E.g 6.000 has 4 SD
What are the steps to convert a number from standard notation to scientific notation?
Try 4769.0550
- How many SD’s? 8
- How many spots to shift the decimal place to get a number between 1-10? 3 to get 4.7690550, the value a
- Use that shift number as the exponent b
- if shift is to ur left b is positive, but if b is to ur right b is negative - Result: 4.7690550 x 10 to the power of 3
Are trailing zeros in scientific notation important?
E.g 2.0000
Yes. This means there are 5SD’s
What 2 things tell us the ‘order of magnitude’ of a value?
The size and sign
E.g 4.5 x 10 to the power of 17 is 3 x 10 (1000) times greater than 4.5 x 10 to the power of 14
That 3 x 10 means ‘3 orders of magnitude’ (where the order of magnitude is the number of powers of 10)
Hint:
A positive b exponent means the value is >1
A negative b exponent means the value is always smaller than <1
What are the base units (units for measurement) for length, mass and time?
Length: meter (m)
Mass: kilogram (kg)
Time: seconds (s)
What is SI?
System internationale units- Standard units for measurement
When using SI units what 2 options can I use?
- Use scientific notation and keep standard unit
- Convert value to a non-SI unit that is derived from the base unit and uses a prefix to relate the size to the base unit
E.g 7 x 10 to the power of -3 or 7 millimeters
What are prefixes?
The word for a value
E.g KILO = 1000 = 10 to the power of 3
What are variables?
Parameters that are not constant in magnitude
2 or more variables may have a ‘cause and effect’ relationship
- The causative variable is termed independent
- The affected variable is termed dependent
When does a proportional relationship exist?
When the causative (independent) variable’s magnitude impacts the affected (dependant) variable’s magnitude in a predictable way
What does the delta symbol (resembles a fish) mean?
Is proportional to
What are the 2 types of proportionality relationships?
Direct and Inverse
Explain direct and inverse relationships?
Direct: The dependant variables magnitude changes in the same direction (bigger or smaller) as the independent variables magnitude change
Inverse: The dependent variables magnitude changes in the opposite direction (bigger or smaller) to the independent variables magnitude change
Notation (way of writing very big/small numbers) for direct and inverse proportionality
Direct:
- Linear relationship A is proportional to B
If B gets x by a number, A will also be x’d by that same number
- Exponential relationship: A is proportional to Bx (power of x)
If B gets x’d by a number, then A will be x’d by that number to an exponent x
Inverse:
-Linear: A is proportional to 1/B
-Exponential: A is proportional to 1/Bx (power of x)
What is the difference between a proportionality statement and an equation?
A proportionality statement answers the question “how do these variables relate”
An equation answers the question “by how much do these variables relate”
- An equation is just a proportionality statement with a constant inserted to make the 2 sides of the equation balance
Where in physics is proportionality used?
As the statements communicate relationships between variables they can be used to predict what will happen to the size of 1 variable when the other’s size is changed, without having to do any actual calculations