Significant Figure and Scientific Notation Review

We have two types of observations in Science: 

Qualitative observations: observations made with the 5 senses. These observations do not include measurements, they are just characteristics. Example: The steel wool turned a dark grey color. 

Quantitative observations: observations that include numbers and measurements. ALWAYS INCLUDE UNITS! :) Example: The steel wool was 4.86 grams.

These measurements all have error! We observed this in our multiple massing experiment. Even though the mass of the object SHOULD NOT change, our measurements had variations. 

On a measurement tool, there are always known or accurate digits and one estimated digit at the end of the measurement. 

For example, if the balance reads 10.04 grams the 10.04 represents the estimated digit.

In measurement, we use two terms to describe the quality of the measurements: 

Accuracy:

Accurate measurements are close to the “true value” or true measurement. 

Precision: Precise measurements are reproducible, but not necessarily close to the true value!

An easier way to express really large or really small numbers.

To express a really larger number like 345,000,000 you move the decimal place to the LEFT until the number in front of the decimal point is between 1-10. 345,000,000. = 3.45 x 10⁸

The number in the superscript is positive for large numbers and the superscript number represents the number of decimal places that the decimal point has moved.

An easier way to express really large or really small numbers.

To express a really small number like 0.000000000123 you move the decimal place to the RIGHT until the number in front of the decimal point is between 1-10. 0.000000000123 = 1.23 x 10^-10

The number in the superscript is negative for small numbers and the superscript number represents the number of decimal places that the decimal point has moved.

ALL measurements have error in them!

A measurement consists of all known digits that can be known accurately PLUS one digit that is estimated.

The estimated digit is always at the end of the number in a measurement.

All of the digits that are known in a measurement are significant figures. Fewer significant figures = more rounding in a measurement = more error.