Significant Figures and Scientific Notation CCT Chemistry and Physics (Apologia)

Scientific Notation Tell how many significant figures, then put into scientific notation: 6.87 Key Point: Scientific notation has the largest place value in the ones place, and every significant figure after it. Sig figs = 3 Sci no = 6.87

More Practice 209 Key Point: Zeroes that come between two non- zero integers ARE significant. Sig figs = * Key Point: Zeroes that come at the end of a number, but after a decimal point ARE significant. Sig figs = * 10 -1

Scientific Notation (cont’d) 200 Key Point: Zeroes at the end of a number, but before the decimal point are NOT significant. Sig figs = 1 2 * Sig figs = *10 2 The only way to indicate that the number 200 actually needs to have 3 significant figures is to use scientific notation: * 10 2

More Practice 2,565 Sig figs = * Key Point: Zeroes that come before non-zero integers are not significant. They are just place holders. Sig figs = *10 -3

Why Bother? Significant figures come from the precision of your tools. Example: My kitchen scale can measure to within one gram. My chemistry scale can measure to within one- hundredth of a gram. Data must reflect the sensitivity of the tools. Key Point: If you are reading graduations on a ruler or graduated cylinder, estimate one significant digit between the lines.

Adding and Subtracting Key Point: Place value matters. Number of significant figures in each number doesn’t. 2, ,927 Both addends are significant to the ones place, so you can report the answer to the ones place.

More Adding and Subtracting 2, ,862 *This is only true in math class! The answer is 2,900! Key Point: Since the place of least significance is the hundreds place in 2,500, the WHOLE answer must be rounded to the hundreds place!

Here’s Where They’ll Trick You What?! The answer of 16 must be rounded to the place of least significance. The number 10 only has one sig fig, in the tens place. The whole answer must be rounded to the tens place!

Multiplying and Dividing Key Point: Count the significant digits in each number in the problem. The answer must have the same number of significant digits as the number with the smallest number of significant digits miles/2.5 hour = miles has 4 sig figs, and 2.5 hours has miles/hour (2.5 hour only has 2 sig figs, so the answer must have 2 sig figs.)

More Multiplying and Dividing 10 *6 60 The number 10 has 1 sig fig, 6 has one sig fig, so the answer 60 also has 1 sig fig. 1.0 * 10 1 * * 10 1 Both 1.0 * 10 1 and 6.0 have 2 sig figs, so the answer must have 2 sig figs. Just 60 has only 1 sig fig, so you must use scientific notation.