Module 00: Introduction, Measurement, and Estimation Flashcards

Question

# Practice Questions 3. (I) Write out the following numbers in full with the correct number of zeros: (a) 8.69 × 10⁴, (b) 9.1 × 10³, (c) 8.8 × 10^–1, (d) 4.76 × 10², and (e) 3.62 × 10^–5.

Answer 1

1. 86900 2. 9100 3. 0.88 4. 476 5. 0.0000362

Answer 2

1. 14,000,000,000 = **1.4 x 10¹⁰ years** 2. 4.4 x 10¹⁷ seconds

Answer 3

*Attachment*

Answer 4

= 9200s + 83000s + 8000s = 100200s = 1.002 x 10⁵ ![]()= **1.00 x 10⁵ s** *(Round to one digit since the value with the fewest significant figures, 0.008, only has one significant figure)*

Answer 5

307.9m \* 0.0068m = 2.09372m ![]() = **2.1** **m²** *(Round to two digits since the value with the fewest significant figures, 0.0068, only has two significant figures)*

Answer 6

Assuming that the uncertainty is one or a few units in the last digit specified, then the 1.57 will have an uncertainty of 1.57 ![]() 0.01, so the measurement is likely between 1.56 and 1.58. Hence, the percent uncertainty is 0.6%

Answer 7

Uncertainty

Answer 8

True Values: **Time, Distance, and Mass** * Important reference in scientific communities * compared to known quantities for the purpose of understanding functions and processes in science

Answer 9

**Error**: Difference between a measured value and true value * Never perfect because measuring devices have limitations **Uncertainty**: Parameter describing the range of values within which the true value lies * Measured and uncertainty must have the same decimal places * *(measured value ± uncertainty range)proper units*

Answer 10

* Caused by improperly calibrated equipment and/or poor instruments * results in consistently high or low values * these errors are easily corrected by recalibrating devices, improving reading techniques, and applying a correction factor to previously recorded measurements

Answer 11

* Limitations of the measurements device and results in measurements * results in unpredictable high and low values * easy to detect statistically but impossible to correct or eliminate. However, performing multiple trials with the same device reduces the uncertainty created by this type of error.

Answer 12

**Accuracy**: * *How close a measured value is to the true value* * Reported quantitatively as percent error * Correlated to systematic error because measurements differ from the true value as a result of this error type **Precision**: * *How close two or more independent measurements agree with each other* * Reported quantitatively as percent uncertainty * correlated to random error because measurements vary from each other as a result of this error type

Answer 13

Increases as the difference between the measured value and expected value increases

Answer 14

increases as the difference between independent measurements increases

Answer 15

**Base Units**: All measurements quantities must be compared to standards understood and referenced throughout the scientific community **Standard Units**: used for measurement in physics adhere to the System International (SI) framework established in 1960 **Derived Units**: further quantification of an object’s properties

Answer 16

* measure larger objects (like a motorcycle) and their properties (like the distance a motorcycle travels) * lack the precision required for measuring smaller objects, such as a grain of sand ## Footnote *most meter sticks are in 1 mm or 0.1 mm graduations*

Answer 17

* precision instrument consisting of a main scale containing one jaw and Vernier scale containing a second jaw that slides along the main scale * The divisions on the Vernier scale indicate the least count or smallest quantity that the instrument can be resolve range between 0.1 mm (about the thickness of a sheet of paper) and 0.05 mm (about the size of the smallest cells in the human body) * The span between the inner jaws measures the inside diameter between two surfaces. The distance between the outer jaws measures the exterior diameters and lengths of objects. * Lastly, the depth probe measures interior depths and lengths of hollow or tubular objects like a soda can * Before measuring an object, the jaws are closed and the alignment of the "0" mark on both the Vernier scale and main scale is noted to determine the zero error * This number indicates the offset of the tool: any offset must be recorded and applied to future measurements. Exterior measurements of an object are taken with a Vernier caliper by first securing the object between the outer jaws. The position of the zero mark on the Vernier scale is noted relative to the main scale and rounded down to the next-smallest mark on the main scale. See Figure 3 for an illustration of the Vernier zero mark positioned between the 20 and 21 mm marks on the main scale. Each Vernier mark is then observed to determine which mark coincides (the Vernier coincidence) with a main scale mark. The number of this Vernier mark represents the fraction of the main scale division that must be added to the recorded measurement. See Figure 3 for an illustration of the Vernier 5 mark that coincides with the main scale 40 mark, resulting in a measurement of 20.50 mm. * As with a meter stick, multiple trials are conducted when measuring objects with Vernier calipers to reduce random error.

Answer 18

_Cube_: **V=a³** Must measure one edge _Sphere_: **V = (4/3)πr³** Must measure the diameter _Cylinder_: **V=πr²h** Must measure the diameter and the height

Answer 19

🔬 **Density**: ratio of the mass of an object to the volume it occupies. * Ratio is the compactness of the substance * Intrinsic property (not vary with amount of a substance) * useful to identify unknown materials by not 100% credited since difference substances are close to each other * Units: g/cm³ Formula: ***ρ=m/V***

Module 00: Introduction, Measurement, and Estimation Flashcards

Lesson 0.1 - Measurement, Uncertainty, Significant Figures Lesson 0.2 - Units, Standards, SI, and Converting Units