Scientific Method & Significant Figures - Vocabulary

Scientific Method: Steps, Concepts, and Applications

• Steps of the Scientific Method

  • 1) Observe natural phenomena and define a problem

  • 2) Formulate a hypothesis

  • 3) Test the hypothesis through the EXPERIMENTATION

  • 4) Record and analyze the data

  • 5) Draw a conclusion

Observation vs Inference

• Observation

  • act of gathering information through the senses

  • Examples from transcript:

  • The workers were laughing.

  • They were eating fried fish and rice.

• Inference

  • explanation or conclusion reached after studying the facts or evidence

  • Examples from transcript:

  • Somebody must have cracked a joke that’s why they were laughing.

  • They were having their lunch break; it was 12 noon.

• Quick exercise (answers from transcript):

  • 1. One worker must be very tired because he is sleeping on his desk. → I

  • 2. Lunch break is not over yet as students are still in the canteen. → I

  • 3. One student was clearing the table. → O

  • 4. Another student was clearing the table. → O

  • 5. The metal felt cold. → O

  • 6. Flowers bloom in the spring. → O

  • 7. It is only 1.5 miles to the park. → I

  • 8. The study hall made no sound. → O

Observation vs Qualitative vs Quantitative

• OBSERVATION QUALITATIVE vs QUANTITATIVE

  • Qualitative: Data gathered directly through the senses; deals with description; cannot be measured directly with numbers.

  • Quantitative: Data gathered using tools (ruler, balance, thermometer); deals with numbers; can be measured/counted.

• Examples:

  • Qualitative: The candle is white and cylindrical.

  • Quantitative: The candle is 15 cm long.

• Classification exercise (as in transcript):
  1) The candle wick is white. → Qualitative
  2) The wick is made up of 3 pieces. → Quantitative
  3) There are 3 colors in the flame of the candle. → Quantitative
  4) After burning, the final length of the candle is 3 cm long. → Quantitative
  5) The candle flame is teardrop-shaped. → Qualitative

Formulating the Research Problem and Variables

• A good research PROBLEM must be:

  • stated as a question

  • clear, concise, with specific, testable variables (IV and DV)

• Observation → Problem statement example:

  • Observation: Leaves of an indoor plant are turning yellow.

  • Problem: How does _ affect ___?

• Problem format (example):

  • How does sunlight affect the color of the leaves of a plant?

  • What is the effect of sunlight on the growth of the plant?

• Independent Variable (IV)

  • variable that is changed or manipulated

  • ext{IV} = ext{variable to be manipulated}

• Dependent Variable (DV)

  • variable which is measured (also known as the response variable)

  • ext{DV} = ext{variable observed/measured}

• Variable (definition)

  • a factor to be manipulated, observed and measured

  • ext{variable} = ext{factor to be manipulated, observed and measured}

• Example:

  • Research question: How does sunlight affect the color of the leaves of a plant?

  • IV: sunlight

  • DV: color of the leaves

Hypothesis

• Definition: a tentative answer to the problem at the start of the investigation; an educated guess

• Example formats:

  • If the plant receives sunlight, then the leaves of the plant will not dry up.

  • The plant needs sunlight in order to stay fresh and green.

• Hypothesis form (IF-THEN):

  • ext{If } ext{sunlight is given}, ext{ then leaves will not dry up.}

• Alternative phrasing (non-IF-THEN):

  • The leaves stay green when the plant receives sunlight.

• IF & THEN HYPOTHESIS example:

  • Does the amount of salt affect the time it takes water to freeze?

  • Hypothesis: ext{If salt is added to water, then the water will take longer to freeze.}

Experiment Design: Control, Experimental Groups, and CV

• An experiment consists of:

  • Control Group: all factors kept constant; depicts the normal/order of things; used for comparison.

  • Experimental Group: differs from Control by at least 1 variable that is manipulated.

• CONSTANT VARIABLES (CV) or CONTROL VARIABLES

  • Remain the same throughout the experiment, helping to isolate the effect of IV on DV.

• Example setup for the plant sunlight problem:

  • Two plants of the same type, same age, same height, same soil, given the same amount of water.

Data Recording and Data Analysis

• Data collected during observations and experiments are recorded in tables, charts, and graphs.

• Example (Table 1): Height comparison between indoor and outdoor plants over days

• Table caption: Table 1 - Comparison Between Indoor & Outdoor Plants in terms of HEIGHT

• Conclusion is drawn from data interpretation and may or may not support the hypothesis. Repeating the experiment and refining the procedure can yield new information and lead to the development of a theory.

Conclusions, Theories, and Laws

• Does NOT support the Hypothesis: conclusions are drawn from data interpretation; may lead to repeating the experiment, adjusting the procedure, or planning a new experiment.

• Does support the Hypothesis: the experiment is repeated for validation; results are published for other scientists to test.

• Theory: When many scientists perform similar experiments and obtain consistent results, the idea can become a THEORY.

• Scientific LAW: Describes patterns consistently observed in nature; can be treated as natural truth. Laws explain behavior of nature but may be revised or discarded with new information; they are not necessarily permanent.

RADISH Seed Experiment: Check Your Understanding (Karlo)

• Scenario: Karlo designed an experiment using 125 radish seeds and 5 petri dishes. Each dish had a filter paper moistened with 5 mL of water. He placed 25 seeds in each dish and recorded results after four days.

• 6) Which question is the student trying to answer?

  • b. Does light intensity affect the number of seeds that sprout?

• 7) The temperature that resulted in the greatest number of sprouted seeds? 30°C

• 8-11) Give at least 4 constant variables (examples):

  • Light intensity (fixed at 1500)

  • Seed type (radish seeds)

  • Number of seeds per dish (25)

  • Volume of water per dish (5 mL)

  • Dish type/size and paper type (filter paper) [and possibly the same dish arrangement across trials]

• 12) What is the IV (independent variable)? Temperature (°C)

• 13) What is the DV (dependent variable)? Number of seeds that sprout

• 14) Which dish number is the control group? Dish 3 (30°C with 1500 lx) is treated as the reference in the transcript; however, the transcript marks dish 3 as a key data point; the conventional control is the baseline condition without manipulations; in this context, dish 3 is identified as the control for the temperature level in the given data set.

• 15) Which dish numbers are the experimental groups? Dishes 1, 2, 4, and 5

• Correct answers (from transcript):

  • 1) Experiment

  • 2) Identify a Problem

  • 3) Conclusion

  • 4) Presentation and analysis of Data

  • 5) Hypothesis

  • 6) C (Constant variables)

  • 7) 30°C

  • 8) filter paper

  • 9) amount of water

  • 10) light intensity

  • 11) number radish seeds

  • 12) temperature

  • 13) amount of seeds that sprout

  • 14) Dish number 3

  • 15) Dish numbers 1, 2, 4 & 5

Significance Figures: Concepts and Rules

• Lesson objectives

  • Define significant figures

  • Calculate the number of significant digits in numbers

  • Round numbers to proper significant digits

  • Apply rules of significant figures in mathematical operations

  • Be accurate or truthful in measurement reporting

• What is Accuracy? vs Precision

  • Accuracy: closeness to the true value

  • Precision: reproducibility/consistency of results

  • Visual aid: darts illustrations show different combinations of accuracy and precision

• Why significant figures matter

  • They communicate the precision of measurements

  • They influence rounding and final reported values

• Key definitions

  • Significant Figures (sig figs): digits that carry meaningful information about precision

  • The last digit is usually the uncertain one

Rules for Determining Significant Figures (5 rules)

1) All nonzero digits are significant.

• Examples: 6 (1 sig fig), 17 (2 sig figs), 183 (3 sig figs), 34.25 (4 sig figs), 12 (2 sig figs), 375 (3 sig figs)
  2) Zeros between nonzero digits are significant.

• Examples: 101 (3 sig figs), 1003 (4 sig figs) [zeros between nonzero digits count]
  3) Zeros at the beginning of a number (leading zeros) are not significant.

• Examples: 0.00123 has 3 sig figs; the leading zeros do not count
  4) Trailing zeros are significant only if the number contains a decimal point.

• Examples: 5.0 (2 sig figs), 5.00 (3 sig figs); 40 (ambiguous without a decimal point)
  5) Zeros at the end of a measurement and to the left of an omitted decimal point are ambiguous; they are not necessarily significant unless indicated by context (e.g., scientific notation or a decimal point).

• Example: 1200 could have 2, 3, or 4 sig figs depending on the measurement context

  • Quick reference guide from slides (examples):

  • Nonzero digits are always significant; zeros between nonzero digits are significant; leading zeros are not; trailing zeros require a decimal to be guaranteed significant; trailing zeros without a decimal can be ambiguous.

Significance Figures in Practice (numbers and exercises)

• Significance figures in a few common cases:

  • 0.00035 → 2 sig figs

  • 105.30 → 5 sig figs

  • 750000 → 2 sig figs

  • 1,000,000 → 1 sig figs

  • 0.00000810 → 3 sig figs

• Practice exercises (typical intent from slides):

  • Identify the number of significant figures in various numbers (examples include cases like 7.1, 0.367, 2.0004, 8.00×10^3, etc.).

  • The goal is to determine how many digits are significant in each given number

Rounding Rules (Significant Figures and Decimal Places)

• Rounding to a specified number of significant figures:

  • Example highlights from slides: rounding to 2 SF, 5 SF, etc. (procedural guidance provided)

• Rounding to decimal places (for addition/subtraction):

  • The final answer must have the same number of decimal places as the quantity with the least decimal places among those being added/subtracted.

  • Example rule: When adding/subtracting, keep the least precise decimal place among the addends.

• Rounding to decimal places (for multiplication/division):

  • The final answer should have as many significant figures as the smallest number of significant figures among the factors.

• Examples from practice problems (selected):

  • Addition/subtraction example: 53.76 + 17.8 + 0.0625 → 71.6 (rounded to the least precise decimal place among the addends, tenths)

  • Another addition example: 278 + 12.8 + 6.79 → 298 (rounded to whole number, as the least precise has no decimals)

  • Mixed example: 3.6439 − 0.88 → 2.76 (rounded to two decimal places in the transcript's context)

• Multiplication/division examples:

  • 4.5 × 8.30 = 37.35; rounded to 2 sig figs → 37

  • 89.36 ÷ 51.2 = 1.745…; rounded to 3 sig figs → 1.75

• More practice problems (as shown in slides):

  • Involves computing with decimals and then rounding according to the rules above; a mixed set of problems demonstrates both rules (addition/subtraction and multiplication/division).

• Final note on rounding:

  • When in doubt, apply the explicit rule for the operation you are performing (add/subtract vs multiply/divide) and report to the appropriate precision.

Inspirational Note

• "Do not judge me by my successes, judge me by how many times I fell down and got back up again." – Nelson Mandela

Quick Reference: Key Symbols

• Independent Variable (IV): ext{IV} = ext{variable to be manipulated}

• Dependent Variable (DV): ext{DV} = ext{variable measured}

• Constant/Control Variable (CV): invariants kept throughout the experiment

• Hypothesis format (IF-THEN):

  • ext{If } X ext{ is varied, then } Y ext{ will change in a predicted way.}

• Example hypotheses from transcript:

  • ext{If sunlight is given to a plant, then the leaves will stay green.}

  • ext{If salt is added to water, then the water will take longer to freeze.}

• Data representation: Tables, charts, and graphs are used to record and analyze data.

• Theoretical progression: Observation → Problem → Hypothesis → Experimentation → Data Analysis → Conclusion → Theory → Law (as appropriate, based on reproducible evidence).