Topic 1 Physical Measurements

1.1 - Orders of Magnitude

Scientific Notation

When recording values for quantities we often use scientific notation.

We always write a number as a number between 1 and 10 with 2 or 3 significant figures followed by an exponent of 10.e.g. the speed of light is 299742548 ms-1

In Sci. this is 3.00x108 ms-1

We use an appropriate number of sig figs based on the instrument made to make the measurement.If in doubt, choose 3 sig figs

Scientific Notation

Write the following values in scientific notation.The mass of a peanut = 1.6084g

Two hectares of land = 20000m2

Seconds in a year = 31556926s

The atomic clock frequency = 9192631770Hz

Working with Scientific Notation

Addition and SubtractionMultiply the number with the larger exponent repeatedly by 10 until the exponents are the same.

Now simply add or subtract the numbers

Finally simplify back into Scientific Notationexample4.1x102 + 3.8x103 = (4.1 + 38)x102 = 42.1x102 =4.21x103question

Find: 6.8x1099 4.5x1097

Working with Scientific Notation

Multiplication and DivisionMultiply or divide the numbers in the normal way.

If multiplying then ADD the exponents; if dividing then SUBTRACT the exponents

Finally simplify back into Scientific notation.Example1.5x10-5 x 4.0x102 = (1.5 x 4.0)x10(-5 + 2) =6x10-3 Question

Find: 8x1078 / 5x1045

Orders of Magnitude

Often, we only want to compare the orders of magnitude of two quantities.

The order of magnitude is simply the exponent part of scientific notation.Think of it as a inaccurate approximation.

We use the tilde ~ to signify order of magnitude.ExampleThe speed of light is 299742548ms-1. Its order of magnitude is ~108ms-1

Orders of Magnitude

Use WolframAlpha (http://www.wolframalpha.com) to find values of (in Sci.) and the order of magnitudes of:The atomic diameter of iron

The nuclear diameter of lead

The size of visible Universe.

The mass of the electron.

The mass of the Universe.

The age of the Universe.

Comparing orders of magnitudes allows us to work out how many times bigger something is.ExampleHow many times smaller is the nucleus than an atom?

10-15 / 10-10 = 10-5 times smaller OR 5 orders of magnitude.Questions

How many times more massive is the Universe than an electron?

How many times older is the Universe than the passage of light across an atom?

How many times smaller is ?

Estimation

Using your experience of the world estimate in Scientific notation and order of magnitude:The length of a 747 Jet

The area of a tennis court

The mass of a basketball

The height of an average man

The mass of an average man

The mass of an average car.

John Kennedy