Mathematics and Scientific Thinking Chapter 1 Lesson 3 Page 22

Math in Science? Good math skills are essential for scientists to collect and analyze data about their subjects! When collecting data, scientists use math skills that include estimation, accuracy, and precision, and significant figures.

Estimation Estimate- an approximation of a number, based on a reasonable assumption Estimation is useful when it is impossible to count every individual or object. It is useful when the thing being measured cannot be measured directly also

Accuracy and Precision Scientists want to make measurements that are accurate and precise! Accuracy- how close the measurement is to the true or excepted value Precision- how close a group of measurements are to each other Scientists try to use the most sophisticated tools/technology to help make the most accurate measurements

Significant Figures Also called Sig Figs High Quality tools allow us to make relatively precise measurements, but they cannot ever be completely precise (always room for error) There are rules that must be followed when adding/subtracting and multiplying/dividing sig figs.

Sig Figs Rules for counting significant figures are summarized below. All Numbers 1-9 are sig figs! There are different rules for when 0 becomes a sig fig.

Sig Fig Zeros become sig figs when: Zeros within a number are always significant. Both 4308 and contain four significant figures. Zeros that do nothing but set the decimal point are not significant. Thus, 470,000 has two significant figures. Trailing zeros that aren't needed to hold the decimal point are significant. For example, 4.00 has three significant figures.

Adding/Subtracting Sig Figs When you add or subtract measurements, the answer must have the same number of digits after the decimal as the measurement with the fewest number of digits after the decimal in the problem. Look at the example on page 25 in the yellow box

Multiplying and Dividing When you multiply or divide sig figs, the answer must have the same number of sig figs as the number with the smallest number of sig figs. Remember when zeros are or are not sig figs!!!!! Look at the example in the green box on page 25

Sig Figs

Math Tools Scientists Use Scientists use many math tools to analyze data, including mean, median, mode, and range. They also use percent error and other math tools to determine if the values of data points are reasonable. Page 27

Mean, Median, Mode They are called measures of central tendency All data tends to center around each of these values Mean- average Median- number in the middle Mode- number that appears the most Look at page 27

Reasonable and Anomalous Data Does that data make sense????? Anomalous Data- data that does not fit with the rest of the data set If a scientist notices any data that is different, he/she should go back and check to see if an error was made ( by the scientist or the equipment) This can also happen due to unknown variables.

Percent Error Some properties never change! If you get a difference when doing calculations of measurements, the difference maybe due to percent errors Errors usually have to do with the accuracy of the equipment being used Percent error- the percent difference between the known value of a substance and the measured value during an experiment

Percent Error A low percent error means that the experimental results were accurate. A high percent error means that the results were inaccurate Percent errors are always considered positive even if the calculation comes out negative

Percent Error Equation Percent error = exp. Value – true value x 100% true value Look at page 29 Answer the questions in the book from page all