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Scientific notation

Scientific notation. a great way for writing really big numbers. Instead of. 602,300,000,000,000,000,000,000. move decimal until there’s ONE DIGIT to the left of it. you could write:. 6.02 x 10 23. stem. exponent. 6.02 x 10. 23. base.

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Scientific notation

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  1. Scientific notation a great way for writing really big numbers. Instead of ... 602,300,000,000,000,000,000,000 move decimal until there’s ONE DIGIT to the left of it you could write: 6.02 x 1023

  2. stem exponent 6.02 x 10 23 base every number in scientific notation has three parts: the stem the base the exponent

  3. stem it’s also great for really small numbers, like 0.000 000 000 000 000 000 000 000 000 000 000 034 3.40 x 10-35 the stem the base the exponent

  4. Significant Digits 7 x 103 = 7000 7.043 x 103 = 7043

  5. 1, 487,328 = 1.487328 x 106 7 sig. digs 1.48733 x 106 1, 487,328 = 6 sig. digs 1.4873 x 106 1, 487,328 = 5 sig. digs 1.487 x 106 1, 487,328 = 4 sig. digs 1.49 x 106 1, 487,328 = 3 sig. digs 1.5 x 106 1, 487,328 = 2 sig. digs 1 x 106 1, 487,328 = 1 sig. digs

  6. If you say 1.000 x 103, you actually MEAN: It’s 1000, and I can actually measure it down to the 1’s So the real actual measurement is between 999.5 and 1000.5 (the span is 1) That’s FOUR sig digs. If you say 1.0 x 103, you actually MEAN: It’s 1000, and I can actually measure it down to the 100’s Somewhere between 9950 and 1050 (the span is 100) That’s 2 sig digs If you say 1 x 103, you actually MEAN: It’s somewhere between 500 and 1500 (the span is 1000) That’s ONE sig.dig.

  7. Multiplying... you can quickly multiply very daunting numbers for example, with NO CALCULATOR, multiply the following: 137,445,000,000,000,000,000,000 x 342,223,111,000,000,000,000,000 = 3 x 1046 = (1 x 1023) x (3 x 1023) • Put in sci notation, 1 sig dig • MULTIPLY the bases • ADD the exponents • Write in proper sci notation

  8. subtract 3 from exponent.... divide by 1000 or ... subtract 3 zeros or... subtract 3 from exponent... divide by 1000 or ... subtract 3 zeros or... m meters nm nanometers one billionth um micrometers one millionth mm millimeters one thousandth km kilometers one thousand Mm megameters one million Gm gigameters one billion add 3 zeros or mult by 1000 or add 3 to exponent add 3 zeros or mult by 1000 or add 3 to exponent examples: 6.7 m is ___ um? 6,700,000 or 6.7 x 106 um 42 um is ____ Mm? 42 x 10-12 Mm or 4.2 x 10-11 Mm 77 km = ____ mm? 77 x 106 mm = 7.7 x 107 mm rem: numbers in scientific notation always have a stem, a base, and an exponent. The stem always has one digit to the left of the decimal. the number of digits to the right of the decimal in the stem depends on the number of significant digits. in most science applications, 3 significant digits is sufficient – one digit to the left and 2 digits to the right of the decimal point. example: 2.45 x 1012 or 6.02 x 1023 or 4.00 x 10-14

  9. SI exponents MEMORIZE these: billionth millionth thousandth thousand million billion nano- micro- milli- (base measurement – e.g. meter) kilo- mega- giga-

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