2 1 n o s s s c

2. 1 n o s s s c i s Le y h P n i s t n e m e r u s ea M Essential Question: What are the basic SI units?

• What are some tools you use for measuring objects? • What are some units of measurement?

Is it a number or a measurement? • In science, measurements are more than just a number. • The kind of physical quantity represented by a certain measurement is called dimension.

What is the measurement system for physics? • The Systeme International d’Unites (SI) is the system of units scientists agreed on for measurements. • There are only seven base units. These units can be combined to form derived units. • It is referred to as the meter-kilogram-second system.

Units of Measurement in SI Measurement Length Mass Time Unit Abbreviation meter kilogram second m kg s Force Energy Pressure newton joule pascal N J Pa Electric current Magnetic flux density ampere tesla A T Electric charge coulomb C

What about extremely small or large numbers? • A lot of times numbers are written as powers of ten. • There are prefixes for certain powers of ten. • The SI uses prefixes to accommodate these extremes.

Prefixes for Powers of 10 in the Metric System Power Prefix Abbreviation attoa deci- d femto- f deka- da pico- p kilo- k nanomicromillicenti- n megagigaterapeta- M G T P exa- E μ m c

Can you convert these? • Converting a measurement from a prefix is easy to do. • Set the prefix equal to 1 m. • To convert measurements, use the conversion factor that will cancel with the units you are given to provide the units you need.

Dimensions and Units Agree • Measurements of physical quantities must be expressed in units that match the dimensions of that quantity. • Measurements used in calculations should also have the same units.

A typical bacterium has a mass of about 2. 0 fg. Express this measurement in terms of grams and kilograms.

A human hair is approximately 50 μm in diameter. Express this diameter in meters.

If a radio wave has a period of 1 μs, what is the wave’s period in seconds?

A hydrogen atom has a diameter of about 10 nm. a) Express this diameter in meters. b) Express this diameter in millimeters. c) Express this diameter in micrometers.

What about accuracy and precision? • Accuracy is a description of how close a measurement is to the correct or accepted value of the quantity measured. • Precision is the degree of exactness of a measurement.

How can you reduce error in experiments? • Take repeated measurements • Use the same method of measuring (method error) • Use proper equipment and tools (instrument error)

How precise can you measure? • Precision is how exact a measurement can possibly be. • You can only be as precise as the instrument you are using. • Significant figures help indicate precision.

What are significant figures? • Those digits in a measurement that are known with certainty plus the first digit that is uncertain. (Actually measured) • The number of significant figures is determined by the precision of the markings on the measuring scale.

• Writing numbers in scientific notation will help determine the number of significant figures. • In scientific notation, the measurement is recorded to a power of 10, and all of the figures given are significant.

Rules for Zeros • Zeros between other nonzero digits are significant. • Zeros in front of nonzero digits are not significant. • Zeros that are at the end of a number and also to the right of the decimal are significant. • Zeros at the end of a number but to the left of a decimal are significant if they have been measured or are the first estimated digit.

What about when you perform a calculation? • Significant figures in calculations have special rules. • The number of significant figures in your result depends on the number of significant figures in each measurement. • Final answers can’t be more precise than the least precise measurement used.

When you multiply or divide… • The result has the same number of significant digits as the original number that has the fewest significant digits. • A rocket traveled 10. 0 m in 7. 0 seconds. How fast did it travel?

When you add or subtract… •

What about calculators? • Calculators don’t pay attention to significant figures. They show as many digits as the display will allow. • Providing answers with the correct number of significant figures often requires rounding the results of a calculation.

How do you round? • Round down when… – The digit following a significant figure is a 0, 1, 2, 3, or 4 • 30. 24 becomes 30. 2 – The last significant figure is an even number and the next digit is a 5, with no other non zero digits • 32. 25 becomes 32. 2 • 32. 6500 becomes 32. 6

• Round up when… – The digit following a significant figure is a 6, 7, 8, or 9 • 22. 49 becomes 22. 5 – The digit following the last significant figure is a 5 followed by a nonzero digit • 54. 7511 becomes 54. 8 – The last significant figure is an odd number and the next digit is a 5, with no other nonzero digits • 54. 75 becomes 54. 8 • 79. 3500 becomes 79. 4

• What are the basic SI units?