MEASUREMENT

Quantities and Units A quantity is anything that can be measured. To identify the thing that is being measured a unit of measurement is used. In science, the accepted system of units used is the S.I. (Système International d'Unités) is used.

Two Types of Basic Quantities There are two (2) types of basic or fundamental quantities used in science: Base quantities are those quantities that are common to any object. Derived Quantities are quantities formed by combining two or more base quantities (using multiplication or division).

BASE QUANTITIES Length (l) Mass (m) Time (t) Temperature (T) Current (I) Light Intensity Amount of Substance

Derived Units Name of Quantity Formula Derived Units Area Length x Breadth Metre-squared ( 𝑚 2 ) Volume Length x breadth x height Metre-cubed ( 𝑚 3 ) Speed Distance / Time Metre per second ( 𝑚 𝑠 −1 ) Pressure Force / Area Newton per metre squared (N 𝑚 −2 ) Pascal (𝑃𝑎)

Prefixes Used Prefix Symbol Value Multiple Kilo Mega Giga Tera K M G T 10 3 10 6 10 9 10 12 Submultiple Deci Centi Milli Micro Nano pico d c m μ n p 10 −1 10 −2 10 −3 10 −6 10 −9 10 −12

Scientific Notation or Standard Form Standard index form is also known as standard form. It is very useful when writing very big or very small numbers. In standard form, a number is always written as: A × 10 n A is always between 1 and 10. 𝑛 tells us how many places to move the decimal point.

Examples The distance of the Earth from the Sun is 149,597,870,700 m (92.956 million miles). Write this in scientific notation. The diameter of an atom is 0.0000000001 m. Write this in standard form.

Length Metre (m) Kilometre (km) = 10 3 𝑚 Centimetre (cm) = 10 −2 𝑚 Millimetre (mm) = 10 −3 𝑚 Micrometre (micron) (μm) = 10 −6 𝑚 Nanometre (nm) = 10 −9 𝑚

Mass Kilogram (kg) Gram (g) = 0.001 kg The international prototype kilogram (the inch ruler is for scale). The prototype is manufactured from a platinum–iridium alloy and is 39.17 mm in both diameter and height.

Measuring Mass Beam Balance Lever Balance Digital Top-Pan Balance

TIME Second (s) Millisecond (ms) = .001 s Microsecond (μs) = .000001 s Nanosecond (ns) = Light year (ly) A light-year is a unit of distance. It is the distance that light can travel in one year. Light moves at a velocity of about 300,000 kilometers (km) each second. So in one year, it can travel about 10 trillion km.

Vernier Scales and Micrometers Lengths can be measured with a ruler to an accuracy of about 1 mm. Some investigations may need a more accurate measurement of length, which can be achieved by using a vernier calipers or a micrometer screw gauge. Micrometer Screw Gauge Vernier Caliper

How to use a Vernier Caliper

How to use a Micrometer Screw Gauge

Errors/Uncertainties in Measurement Errors/uncertainties in measurement can be due to a number of factors, including: The limitations of the measuring instrument Variations in how the measurements are made The conditions of the experiment The common types of error in measurements are: Errors due to parallax Systematic errors

Parallax Error

Systematic Errors

Term Used in Experimental Physics Range refers to the size of the interval between the maximum and minimum quantities that a measuring instrument can measure. Sensitivity (resolution) measures the response of an instrument to the smallest change in input. The greater the response to a small change, e.g, in voltage or current, the greater the sensitivity Accuracy is how close the experimental value is to the true value. Accuracy is improved if errors due to measuring instruments and experimental procedures are identified and their effect reduced.

Precision refers to how small an uncertainty the measuring instrument will give. For example, a thermometer marked at every degree will give a more precise reading than one marked at every 5 degree interval. Linear Scale: scales where the marks are evenly spaced. Non-linear Scales: the markings are not evenly spaced making it difficult to read between 2 points on the scale