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Scientific Notation

Scientific Notation. Scientists work with large and small numbers. These numbers take up to much space and are hard to put into calculators. We use shorthand where we express decimal places as power of 10. M x 10n where 10> M >/=

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Scientific Notation

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  1. Scientific Notation • Scientists work with large and small numbers. These numbers take up to much space and are hard to put into calculators. We use shorthand where we express decimal places as power of 10. M x 10n where 10> M >/= and n is an integer

  2. Move the decimal until only 1 non-zero digit remains on the left. Next count how many places the decimal has been moved and use the number as the exponent of 10. • Remember • the exponent becomes larger as the decimal moves to the left • the exponent becomes smaller as the decimal moves to the right

  3. Significant Digits (Figures) • Uncertainty in measurements: Due to two things: • external causes – the device used may be inaccurate (metal rulers expands with temperature or electronic devices are affected by magnets) • human error – this is caused by parallax (the apparent shift in the position of an object when it is viewed from various angles) • SIGNIFICANT DIGITS – all the digits that are certain plus a digit that estimates the fraction of the smallest division of the measured scale.

  4. Identifying Significant Digits • There are 4 rules for identifying significant digits: • all non-zero digits are always significant • all zeros between two non-zero digits are significant • zeros after the decimal and last in the number are significant • zeros after the decimal and first in the number are not significant (place holders)

  5. Operations with Significant Digits • The result of any mathematical operation with measurements can never be more precise that the least precise measurements (2 rules) • When adding and subtracting you can find the least precise measurement by counting the places after the decimal. The measurement that has the smallest number of digits after the decimal is least precise and your answer can have no more places that this one. • When multiplying and dividing you can determine the least precise measurement by counting the significant digits it has. The least precise measurement is the one with the least sig. figs. Your answer can have no more sig. figs. than this measurement .

  6. Metric System • The Metric System • Created by a French scientist in 1795 • Convenient to use because its units are related by powers of 10 • International system if units (SI) • Fundamental units • meter (m) SI unit of length • second (s) – SI unit of time • kilogram (kg) – SI unit for mass

  7. metric prefixes large measurements tera giga mega kilo hector deka meter T G M k h da root 1012 109 106 103 102 101 100 small measurements deci centi milli micro nano pico d c m μ n p 10-1 10-2 10-3 10-6 10-9 10-12

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