Measurement & Precision MacInnes Science

Quantitative vs. Qualitative Quantitative observation is using numerical data such as a measurement or how many minutes or degrees “It took two hours to ride from the start to the end of that route.” Qualitative observation is the quality of something such as shape or colour or can be a more subjective observation “It took a long time to ride this route.”

Qualitative or Quantitative? 1. The cup of tea was very hot. 2. The refrigerator cooled the orange juice by 18 degrees Celsius. 3. The electric guitar was louder than the acoustic guitar. 4. Ethanol is very flammable 5. The speed limit in a school zone is 40km/h 6. The solution had a pH of 5.2.

Precision & Accuracy No measuring device can give an absolutely exact measurement. Precision describes both the exactness of a measuring device and the range of values in a set of measurements. Accuracy is how close a measurement or calculation comes to the true value. To improve accuracy, scientific measurements are often repeated.

Precise & Accurate? 1. A student measures the temperature of ice water four times, and each time gets a result of 10.0°C. Is the thermometer precise and accurate? Explain. 2. Two students collected data on the mass of a substance for an experiment. Each student used a different scale to measure the mass of the substance over three trials. Student A had a range of measurements that was ±0.06g. Student B had a range of measurements that was ±0.11g. Which student had the more precise scale?

Accuracy of measurement The volume (amount of space an object occupies) of a liquid can be measured directly as shown in the diagram. We must make sure to measure to the bottom of the meniscus (the slight curve where the liquid touches the sides of the container). To measure accurately, your eye must be at the same level as the meniscus.

What is the volume?

Significant digits Significant digits (or figures aka Sig Figs) represent the amount of uncertainty in a measurement. The significant digits in a measurement include all the certain digits plus the first uncertain digit. In the example, the length of the object is between 2.5 cm and 2.6 cm. The first two digits are certain (2 and 5 – we can see those marks), but the last digit (5) was estimated, so it is uncertain. So 2.55 cm has three significant digits. In the other example, only the 2 is certain so the 5 is uncertain and 2.5 cm has two significant digits.

Rules for counting significant digits 1. All non-zero digits (1-9) are considered significant. 2. Zeros between non-zero digits are also significant. Ex: 1207 (4 s.d.); (4 s.d.) 3. Any zero that follows a non-zero digit and is to the right of the decimal is significant (4 s.d.); (4 s.d.) 4. Zeros used to indicate the position of the decimal are not significant. 500 (1 s.d.); (3 s.d.); (2 s.d.); (3 s.d.)

How many significant digits? cm km/h m km mm cm² m m cm m

Rules for rounding When the first digit to be dropped is less than 5, round down (the digit remains unchanged). When it is more than 5, increase the digit (round up) m rounded to two significant digits is 6.7 m If the digit to be dropped is 5, round to the nearest even number m rounded to three significant digits is 7.24 m

Rounding in mathematical operations When adding or subtracting, round off the answer to the same number of decimal places as the value with the fewest decimal places. Ex: 2.3 cm cm cm = cm = 22.5 cm (1 decimal place was the smallest) When multiplying or dividing, round off the answer to the least number of significant digits. Ex: (2.342 m)(0.063 m)(306 m) = m³ = 45 m³ (2 s.d. was the least)