Question Of the Day:

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Question Of the Day:. Write the following numbers in scientific notation: 0.000412 143.0 12 000 000 000 Convert the following: 1 μ m = m 0.001 A = mA 1hm = m. Answers. Write the following numbers in scientific notation: 0.000412 => 4.12 x 10 -4 143.0 => 1.43 x 10 2 - PowerPoint PPT Presentation

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Question Of the Day:Write the following numbers in scientific notation:0.000412143.012 000 000 000

Convert the following:1 m = m0.001 A = mA1hm = m

PrefixSymbolScientific NotationgigaG109megaM106Kilo k103 hectoh102decada101Base unit [gram (g), meter(m), liter (l), etc.] x100decid10-1centic10-2millim10-3micro10-6nanon10-9picop10-12AnswersWrite the following numbers in scientific notation:0.000412 => 4.12 x 10 -4143.0 => 1.43 x 10 212 000 000 000 => 1.2 x 1010

Convert the following:1 m = 0.000001m0.001 A = 1mA1hm = 100m

PrefixSymbolScientific NotationgigaG109megaM106Kilo k103 hectoh102decada101Base unit [gram (g), meter(m), liter (l), etc.] x100decid10-1centic10-2millim10-3micro10-6nanon10-9picop10-12Significant Figures and Real Life3RULESRule 1: All nonzero numbers are significant.Examples: 4328, 38273, 1234Rule 2: All zeros that are sandwiched or between two nonzero numbers are significant. Examples: 303, 23903, 9401Rule 3: Trailing zeros are significant if the number contains a decimal.Examples: 1290.0, 10890. , 10. , 3000.Not examples: 10, 3000, 870Rule 4: Leading zeros that function only to hold the decimal point are NOT significant. Example: 0.009, 0.65Rule 5: Zeros that are in a decimal number that are after a nonzero digit are significant. Examples: 0.906, 0.8370Rule 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 102Lets Talk About RoundingWhat 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 QuestionWhat 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 000How 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 becomesNow Try These:Write each number 3 sig figs, then put the number into scientific notation!345629320.034990.05 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 cant 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.10

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?Ruler A11Are 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?

12When a measurement is recorded properly, all of the digits that are read directly (certain) and oneestimated (uncertain) digit are called significant digits. The number of allowable significant digits isdetermined by the marks or gradations of the instrument. Sometimes a 0 is the estimated digit andmust be recorded.Rule of Thumb

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Ruler BWhat number(s) are we certain of here?What number(s) is uncertain? Make an estimation of the length of the Mg strip.14

THINK ABOUT ITWhen 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.15Ruler C

What number(s) are we certain of here?What number(s) is uncertain? Make an estimation of the length of the Mg strip.

PRACTICE