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Questions and Answers
How many significant figures are present in the number 39,800?
How many significant figures are present in the number 39,800?
- 5
- 3
- 4
- It depends on context (correct)
What is the significance of trailing zeros in the number 100?
What is the significance of trailing zeros in the number 100?
- They are always significant
- They are not significant in any case
- They are significant if a decimal point is present (correct)
- They count as placeholders only
Which of the following statements about significant figures is correct for the number 0.0017?
Which of the following statements about significant figures is correct for the number 0.0017?
- It has 3 significant figures
- Leading zeros are considered significant
- It has 2 significant figures (correct)
- It has 4 significant figures
Which digit in the number 1,007 is not a significant figure?
Which digit in the number 1,007 is not a significant figure?
How many significant figures does the number 17.00 contain?
How many significant figures does the number 17.00 contain?
In scientific notation, how are significant figures represented?
In scientific notation, how are significant figures represented?
Which of the following numbers has four significant figures?
Which of the following numbers has four significant figures?
Which of the following correctly describes trapped zeros?
Which of the following correctly describes trapped zeros?
What does temperature represent in a scientific context?
What does temperature represent in a scientific context?
Which statement is true regarding heat and temperature?
Which statement is true regarding heat and temperature?
What is absolute zero?
What is absolute zero?
What does the Kelvin temperature scale correspond to in terms of kinetic energy?
What does the Kelvin temperature scale correspond to in terms of kinetic energy?
Who developed the concept of absolute zero?
Who developed the concept of absolute zero?
What is the freezing point of water on the Celsius scale?
What is the freezing point of water on the Celsius scale?
What does the term 'thermal energy' refer to?
What does the term 'thermal energy' refer to?
How does increasing the temperature of a material affect its thermal energy?
How does increasing the temperature of a material affect its thermal energy?
What does scientific notation help to simplify?
What does scientific notation help to simplify?
What is the first step if a scientist finds their original hypothesis to be completely wrong?
What is the first step if a scientist finds their original hypothesis to be completely wrong?
In the number $579,000,000,000$, what is the coefficient when expressed in scientific notation?
In the number $579,000,000,000$, what is the coefficient when expressed in scientific notation?
What indicates how many positions the decimal point is moved in scientific notation?
What indicates how many positions the decimal point is moved in scientific notation?
Which scientific investigation method step is NOT part of the general process outlined?
Which scientific investigation method step is NOT part of the general process outlined?
When expressing a number in scientific notation, what must the coefficient be between?
When expressing a number in scientific notation, what must the coefficient be between?
What impact does scientific notation have on calculations involving very large or very small numbers?
What impact does scientific notation have on calculations involving very large or very small numbers?
What is an example of an exact number?
What is an example of an exact number?
How many significant figures does the number 100.0 have?
How many significant figures does the number 100.0 have?
According to the 'rounding to the even' rule, how should the number 27.55 be rounded to two significant figures?
According to the 'rounding to the even' rule, how should the number 27.55 be rounded to two significant figures?
When dealing with significant figures, how do exact numbers affect calculations?
When dealing with significant figures, how do exact numbers affect calculations?
Which of the following is true about rounding numbers in scientific operations?
Which of the following is true about rounding numbers in scientific operations?
If the number 34.84 is rounded to three significant figures, what is the resulting value?
If the number 34.84 is rounded to three significant figures, what is the resulting value?
What is the correct approach to rounding the number 45.50 to one significant figure?
What is the correct approach to rounding the number 45.50 to one significant figure?
How does the 'rounding to the even' rule prevent bias in large datasets?
How does the 'rounding to the even' rule prevent bias in large datasets?
What is the first step in the Addition/Subtraction rule?
What is the first step in the Addition/Subtraction rule?
How should final answers be rounded according to the Addition/Subtraction rule?
How should final answers be rounded according to the Addition/Subtraction rule?
In the Multiplication/Division rule, what should you do first?
In the Multiplication/Division rule, what should you do first?
What is the purpose of the 'good enough' rule of precision?
What is the purpose of the 'good enough' rule of precision?
What should you do before performing multiplication/division on a complicated problem?
What should you do before performing multiplication/division on a complicated problem?
When converting units, what is an essential step for accuracy?
When converting units, what is an essential step for accuracy?
If a nurse has 50 mg aspirin tablets and needs to administer 0.2 g, how many tablets does she need?
If a nurse has 50 mg aspirin tablets and needs to administer 0.2 g, how many tablets does she need?
What is a risk of using 'good enough' numbers in calculations without tracking significant figures?
What is a risk of using 'good enough' numbers in calculations without tracking significant figures?
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Study Notes
Scientific Method and Hypothesis
- The scientific process often requires formulating and revising hypotheses based on experimental results.
- The scientific method typically includes observation, hypothesis formulation, experimentation, and conclusion.
Scientific Notation
- Scientific notation simplifies the expression of very large or small numbers using powers of ten.
- Example conversion of a large number: 579,000,000,000 is expressed as 5.79 x 10¹¹.
- The exponent in scientific notation indicates how many places the decimal moves from the original number.
Temperature and Thermal Energy
- Temperature measures the average kinetic energy of particles in a substance; it increases with added thermal energy.
- Heat is defined as the transfer of thermal energy from warmer to cooler objects.
- A thermometer, derived from “thermo” (heat) and “meter” (to measure), quantifies temperature changes.
Kelvin Temperature Scale
- Lord Kelvin introduced a scale where absolute zero (0 K) represents the point at which molecular motion ceases.
- The Celsius scale is based on water's freezing (0°C) and boiling points (100°C).
Significant Figures
- Significant figures reflect the precision of measurements; they include all known digits and the first estimated digit.
- Rules:
- All non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros after a decimal are significant.
- Trapped zeros between non-zero digits are significant.
- Exact numbers, such as counted items, do not affect the significant figures in calculations.
Rounding Rules
- Rounding to the even (or "round half to even") method helps reduce bias in large datasets.
- Rounding rules:
- If the last digit dropped is 4 or less, the preceding digit remains unchanged.
- If it is 6 or greater, the preceding digit increases by one.
- If it is exactly 5, the preceding digit is rounded to the nearest even number.
Arithmetic with Significant Figures
- Addition/Subtraction Rule:
- The answer is rounded to the least number of decimal places in any term.
- Multiplication/Division Rule:
- The answer is rounded to the least significant figures from any term involved.
Conversions and Units
- Being proficient in converting units is essential, especially in fields like medicine (e.g., converting grams to milligrams).
- Understanding basic unit equivalencies facilitates accurate dosage calculations and other practical applications.
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