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Write the following numbers in scientific notation: 0.000412 Prefix Symbol Scientific Notation 143.0 giga G 109 mega M 106 12 000 000 000 Kilo Convert the following: 1 μm = m 0.001 A = mA 1hm = m k 103 hecto h 102 deca da 101 Base unit [gram (g), meter(m), liter (l), etc.] x100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 Answers Write the following numbers in scientific notation: Prefix Symbol Scientific 0.000412 => 4.12 x 10 -4 Notation 2 143.0 => 1.43 x 10 giga G 10 M 10 12 000 000 000 => 1.2 x 1010 mega 9 6 Kilo Convert the following: 1 μm = 0.000001 m 0.001 A = 1mA 1hm = 100 m k 103 hecto h 102 deca da 101 Base unit [gram (g), meter(m), liter (l), etc.] x100 deci d 10-1 centi c 10-2 milli m 10-3 micro μ 10-6 nano n 10-9 pico p 10-12 RULES Rule 1: All nonzero numbers are significant. Examples: 4328, 38273, 1234 Rule 2: All zeros that are “sandwiched” or between two nonzero numbers are significant. Examples: 303, 23903, 9401 Rule 3: Trailing zeros are significant if the number contains a decimal. Examples: 1290.0, 10890. , 10. , 3000. Not examples: 10, 3000, 870 Rule 4: Leading zeros that function only to hold the decimal point are NOT significant. Example: 0.009, 0.65 Rule 5: Zeros that are in a decimal number that are after a nonzero digit are significant. Examples: 0.906, 0.8370 Rule 6: If a number is written in scientific notation then all numbers to the left of the multiplication sign are significant. Examples: 1.03 x 102 Let’s Talk About Rounding What if I have the number 245 200 000 and I want it written with only 3 significant figures. Which digit would I have to round? What are the rules of rounding? Rule 1: If the digit you are rounding is followed by a 0, 1, 2, 3, or 4 then the digit you are rounding stays the same. All the digits after the rounded digit becoms zero. For example, if you are rounding 452 to the nearest tens then the number becomes 450. Rule 2: If the digit you are rounding is followed by a 5, 6, 7, 8, or 9 then the digit you are rounding increases by one. All digits after the rounded digit become zero. For example, if you are rounding 452 to the nearest hundreds then the number becomes 500. So… Back to the Original Question What if I have the number 245 200 000 and I want it written with only 3 significant figures. Which digit would I have to round? If I wanted three sig. figs the number would be written as 245 000 000 How could we put 245 200 000 into scientific notation using only 3 sig. figs. 2.45 x 10 8 Another example: Write 0.0003249914 into scientific notation with only 4 sig figs. This becomes Now Try These: Write each number 3 sig figs, then put the number into scientific notation! 3456 2932 0.03499 0.05 WHY? Scientists do a lot of measuring. When scientists use an instrument (such as a ruler, graduated cylinder, spectrophotometer or balance) to measure something, it is important to take full advantage of the instrument. However, they can’t cheat and record a better measurement than the instrument is capable of. There is an understanding among scientists of the proper way to record valid measurements from any instrument. When you are the scientist, you must record data in this way. When you are reading other scientists’ work, you must assume they recorded their data in this way. Example: In a lab we have to measure the length of this Mg strip. Using the ruler, how long do you think this piece of Mg is? Are we certain of these values? From the values listed on the board do you think that there was any agreement between any of these values? When a measurement is recorded properly, all of the digits that are read directly (certain) and one estimated (uncertain) digit are called significant digits. The number of allowable significant digits is determined by the marks or gradations of the instrument. Sometimes a “0” is the estimated digit and must be recorded. Make an estimation of the length of the Mg strip. What number(s) are we certain of here? What number(s) is uncertain? THINK ABOUT IT • When humans use measuring instruments, variation is expected. Everyone will estimate differently between marks on the instrument. On the other hand, digits that are certain (based on marks on the instrument) should not vary from person to person. Make an estimation of the length of the Mg strip. What number(s) are we certain of here? What number(s) is uncertain?