Lesson 1.2 Measurements in Physics 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 Abbreviation Length meter m Mass kilogram kg Time second s Force newton N Energy joule J Pressure pascal Pa Electric current ampere A Magnetic flux density tesla 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 Abbreviation 10 −18 atto- a 10 −1 deci- d 10 −15 femto- f 10 1 deka- da 10 −12 pico- p 10 3 kilo- k 10 −9 nano- n 10 6 mega- M 10 −6 micro- μ 10 9 giga- G 10 −3 milli- m 10 12 tera- T 10 −2 centi- c 10 15 peta- P 10 18 exa- E

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 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 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. Express this diameter in meters. Express this diameter in millimeters. Express this diameter in micrometers.

The distance between the sun and Earth is about 1. 5× 10 11 m The distance between the sun and Earth is about 1.5× 10 11 m. Express this distance with an SI prefix and in kilometers.

The average mass of an automobile in the United States is about 1 The average mass of an automobile in the United States is about 1.440× 10 6 g. Express this mass in kilograms.

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… Line up the decimal points; the last significant digit in the result corresponds to the right-most column where all numbers still have significant digits. 3.6+14+6.33=?

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?