Measurement and Conversions Remember Have fun Importance of

Measurement and Conversions Remember: Have fun!!!

Importance of Measurement Qualitative Measurements • Descriptive nonnumeric form • “Qualities” or physical properties Quantitative Measurements • Definite form, usually as numbers • “Quantities” or How much? /How many?

Accuracy vs Precision /Reproducibility Accuracy • Refers to the closeness of measurements to the correct or true value Reproducibility (Precision) • Refers to the closeness of several measurements to the same value, not necessarily the true value Precision is a measure of exactness of a measurement. The more significant figures, the higher the precision, ex: 4. 02, and 4. 0231 (3. 0 is more precise than just 3)

Accuracy Vs. Reproducibility Scientists aim for both accuracy and reproducibility in their measurements

Significant Figures in Measurement High accuracy, low In Science, measurement reproducibility should be Accurate and Reproducible Accuracy = close to the actual/true value or the target Low accuracy, high Reproducibility refers to Reproducibility how close a group of measurements are to each other .

Significant Figures in Measurement The valid digits in a measurement are called significant digits. Measurements are made with measuring tools that have a calibrated (standardized) scale. The last digit given for any measurement is the uncertain or estimated digit. It is uncertain because it is estimated.

Significant Figures

Why is this important? Significant figures were created to help scientists determine how they should round off their answers. Precision is a measure of exactness of a measurement. The more significant figures, the higher the precision, ex: 4. 02, and 4. 0231 Precise measurements of time are also important in sports. Just ask Phelps and Cavic (50. 58 to 50. 59) Phelps-video

Practice Each of five students used the same ruler to measure the length of the same pencil. These data resulted: 15. 33 cm, 15. 34 cm, 15. 33 cm, 15. 34 cm. The actual length of the pencil was 15. 85 cm. Describe whether accuracy, reproducibility and precision are each good or poor for these measurements.

Measuring to a significant figure (precision) Contain all digits that are known precisely plus one last digit that is estimated How long is the nail?

Significant figures in a measurement Which digits in a measurement are significant? Every nonzero digit Certain zeros are significant See chart

How many significant figures are in each or the following measurements? 123 m 0. 123 cm 9. 80 22. 80 0. 07080 m

Significant Figures in Measuement Measurements are always measured by estimating between the smallest graduation given. The top ruler measures with more precision There is uncertainty in the last digit of a scientific measurement only

Measure each object to a correct significant figure with different rulers

Measure the following to a significant figure Using the ruler below, record the position of the arrow to the nearest m. L. Show the correct number of significant figures.

Scientific Notation A number written as a product of two numbers: a coefficient and a power of 10 Used for very large or very small numbers 3. 6 x 104 Coefficient Power of 10

Scientific Notation 3. 6 x 104 3. 6 x 10 = 36000 = 3. 6 x 104 Decimal moves 4 Exponent is 4 Places to the left

Scientific Notation 8. 1 x 10 -3 8. 1 = 0. 0081 10 x 10 0. 0081 = 8. 1 x 10 -3 Decimal moves 3 places to the right Exponent is -3

SI units of Measurement The International System of Units (SI) Standard of measurement used in science Revised version of the metric system Units based on 10 Seven base units Derived units, such as volume, density etc.

Base units Gram - the measure of mass, the amount of matter (size of a small paperclip) Meter – the measure of length (one large step) Liter – the measure for volume, how much space something takes up (about 4 cups) Newtons- the measure of weight (force of gravity on something) Seconds – the measure of time

Base Units Degrees Celsius or Kelvin measure Temperature Absolute zero is -273. 15 degrees Celsius or 0 degrees Kelvin Nothing is colder than absolute zero

Prefixes that change the value

KHDBDCM Kilo (k)- 1000 Hecto (h)- 100 Deka (da)- 10 Base Unit (m, g, l) 1 Deci (d)– 0. 10 Centi (c) 0. 01 Milli – (m) 0. 001 King Henry Died By Drinking Chocolate Milk! Kings Hate Dragons Because Dragons Chase Maidens

What unit would I use to measure: The length of your desk? The height of the ceiling? The amount of water in a swimming pool? The mass of a pushpin? The mass of a person? The amount of water in a fish tank?

Converting from one unit to another Makes huge numbers make more sense Makes extremely small numbers make more sense Water is what the metric system is based on!! 1 cmᶟ = 1 ml = 1 g

Converting from one unit to another

KHDBDCM Divide by 10 (arrows show the direction to move the Decimal Point) K Kilo H Hecto Multipy by 10 D Deka B Base Unit D C M Deci Centi Milli (Gram, Meter, Liter) Thousand 1000 Hundred 100 Ten 10 _____ One 1 . Tenths . 1 Hundredths . 01 Thousandths . 001 _____

Examples (Dimensional Analysis 1) Convert: (2 meters into centimeters) 2 m=____ cm

Dimensional Analysis 2 Convert: 12 ml = ______ L

Dimensional Analysis 3 Convert: 40 g = _____ Kg