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Section 1.6—Scientific Notation

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Scientific Notation Scientific Notation is a form of writing very large or very small numbers that you’ve probably used in science or math class before Scientific notation uses powers of 10 to shorten the writing of a number.

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Writing in Scientific Notation The decimal point is put behind the first non-zero number The power of 10 is the number of times it moved to get there A number that began large (>1) has a positive exponent & a number that began small (<1) has a negative exponent

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Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m

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Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m 1.24567656 10 m 4 6.5423 10 g -5 1.2890 10 m 2 7.532 10 m -7 The decimal is moved to follow the first non-zero number The power of 10 is the number of times it’s moved

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Tiny original numbers have negative exponents Example #1 Example: Write the following numbers in scientific notation. 12457.656 m 0.000065423 g 128.90 g 0.0000007532 m 1.24567656 10 m 4 6.5423 10 g -5 1.2890 10 m 2 7.532 10 m -7 Large original numbers have positive exponents

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Reading Scientific Notation A positive power of ten means you need to make the number bigger and a negative power of ten means you need to make the number smaller Move the decimal place to make the number bigger or smaller the number of times of the power of ten

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Example #2 Example: Write out the following numbers. 1.37 10 4 m 2.875 10 2 g 8.755 10 -5 g 7.005 10 -3 m

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1.37 10 4 m 2.875 10 2 g 8.755 10 -5 g 7.005 10 -3 m Example #2 Example: Write out the following numbers. 13700 m 287.5 g 0.00008755 m 0.007005 m Move the decimal “the power of ten” times Positive powers = big numbers. Negative powers = tiny numbers

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Scientific Notation & Significant Digits Scientific Notation is more than just a short hand. Sometimes there isn’t a way to write a number with the needed number of significant digits …unless you use scientific notation!

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Take a look at this… Write 120004.25 m with 3 significant digits 120004.25 m 120000. m 120000 m 1.20 10 5 m 120. m 8 significant digits 6 significant digits 2 significant digits 3 significant digits Remember…120 isn’t the same as 120000! Just because those zero’s aren’t significant doesn’t mean they don’t have to be there! This answer isn’t correct!

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Examples #3 Example: Write the following numbers in scientific notation. 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs

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Examples #3 Example: Write the following numbers in scientific notation. 120347.25 g with 3 sig digs 0.0002307 m with 2 sig digs 12056.76 mL with 4 sig digs 0.00000024 g with 2 sig digs Move the decimal after the first non-zero number Start counting significant figures from that first non-zero number Round when you get the wanted number of significant digits Remember—large numbers are positive powers of ten & tiny numbers have negative powers of ten! 1.20 × 10 5 g 2.3 × 10 -4 g 1.206 × 10 4 g 2.4 × 10 -7 g

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Let’s Practice Example: Write the following numbers in scientific notation. 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write out the following numbers 1.34 × 10 -3 g 2.009 10 -4 mL 3.987 10 5 g 2.897 10 3 m

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Let’s Practice 7.7 × 10 -4 g 1.20 × 10 5 g 2.391 × 10 5 g 7.80 × 10 -6 g Example: Write the following numbers in scientific notation. 0.0007650 g with 2 sig digs 120009.2 m with 3 sig digs 239087.54 mL with 4 sig digs 0.0000078009 g with 3 sig digs Example: Write out the following numbers 1.34 × 10 -3 g 2.009 10 -4 mL 3.987 10 5 g 2.897 10 3 m 0.00134 g 0.0002009 mL 39870 g 2897 m

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Chapter 1—Scientists’ Tools Summary

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Chemistry is an Experimental Science You have learned the following: Common characteristics of scientific processes How observations & measurements are taken accurately & precisely during those scientific processes How to design a lab yourself to answer questions How to convert units you’ve measured in to ones that are more useful to calculate with How to report answers to calculations with the correct number of significant digits to represent the accuracy of the measurements you took in the lab How to use scientific notation to express the correct number of significant figures

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What did you learn about Scientists’ tools?

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Chemistry is an Experimental Science Common characteristics Although no one method, there are Careful observation s Accurate & precise measurements Design your own labs Unit conversions Significant digit rules Scientific Notation Are used when you include May require When using in calculations, follow May require using

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