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3:00 2:59 2:58 2:57 2:56 2:55 2:54 2:53 2:52 2:51 2:50 2:49 2:48 2:47 2:46 2:45 2:44 2:43 2:42 2:41 2:40 2:39 2:38 2:37 2:36 2:35 2:34 2:33 2:32 2:31 2:30 2:29 2:28 2:27 2:26 2:25 2:24 2:23 2:22 2:21 2:20 2:19 2:18 2:17 2:16 2:15 2:14 2:13 2:12 2:11 2:10 2:09 2:08 2:07 2:06 2:05 2:04 2:03 2:02 2:01 2:00 1:59 1:58 1:57 1:56 1:55 1:54 1:53 1:52 1:51 1:50 1:49 1:48 1:47 1:46 1:45 1:44 1:43 1:42 1:41 1:40 1:39 1:38 1:37 1:36 1:35 1:34 1:33 1:32 1:31 1:30 1:29 1:28 1:27 1:26 1:25 1:24 1:23 1:22 1:21 1:20 1:19 1:18 1:17 1:16 1:15 1:14 1:13 1:12 1:11 1:10 1:09 1:08 1:07 1:06 1:05 1:04 1:03 1:02 1:01 1:00 0:59 0:58 0:57 0:56 0:55 0:54 0:53 0:52 0:51 0:50 0:49 0:48 0:47 0:46 0:45 0:44 0:43 0:42 0:41 0:40 0:39 0:38 0:37 0:36 0:35 0:34 0:33 0:32 0:31 0:30 0:29 0:28 0:27 0:26 0:25 0:24 0:23 0:22 0:21 0:20 0:19 0:18 0:17 0:16 0:15 0:14 0:13 0:12 0:11 0:10 0:09 0:08 0:07 0:06 0:05 0:04 0:03 0:02 0:01 0:00 Do Now How many sig figs are in the following numbers Solve to the correct # of sig figs x25.100/.0013

Errors in Measurements

Measuring instruments have limitations: It is necessary to estimate one place beyond the finest measurement of the measuring device to get the object’s length. This is always the case. As a result, there are always errors of measurement. The length of this object falls between lines of the ruler.

Consider the following two errors: You fly from New York to San Francisco. Your plane is blown off course by 5 cm. You are an eye surgeon. Your scalpel misses its mark by 5 cm.

The error is 5 cm in each of the previous examples, but they are not equivalent! This type of error is called the absolute error. It is the absolute value of the difference between the measured value and the accepted value. o The accepted value is most probable value or the value based on references o Only the size of the error matters, not the sign.

The absolute error tells you how far you are from the accepted value. It does not tell you how significant the error is. o Being off course by 5 cm on a trip to San Francisco is insignificant, because San Francisco is very big. o Being off by 5 cm in eye surgery means you are operating on the wrong eye. It is necessary to compare the size of the error to the size of what is being measured to understand the significance of the error.

The percentage error compares the absolute error to the size of what is being measured. It is the absolute value of the difference between the measured value and the accepted value all divided by the accepted value and multiplied by 100 %.

Aluminum has a density of 2.7 g / mL. A student measured some aluminum and experimentally determined the density to be 3.5 g / mL. What is the students percent error?

Aluminum has a density of 2.7 g / mL. A student measured some aluminum, and determined that a sample of aluminum with a mass of 21.6 g occupied 4.0 mL. How big is the error? The error is as big as what is being measured!!