By Daniel Fleisch, Julia Kregenow
The learn of astronomy deals a vast chance for us to achieve a deeper figuring out of our planet, the sunlight method, the Milky method Galaxy and the recognized Universe. utilizing the plain-language process that has confirmed hugely renowned in Fleisch's different Student's publications, this booklet is perfect for non-science majors taking introductory astronomy classes. The authors tackle themes that scholars locate such a lot problematical, on topics starting from stars and lightweight to gravity and black holes. Dozens of absolutely labored examples and over one hundred fifty workouts and homework difficulties support readers become familiar with the techniques in every one bankruptcy. An accompanying site incorporates a host of assisting fabrics, together with interactive options for each workout and challenge within the textual content and a chain of video podcasts within which the authors clarify the $64000 innovations of each portion of the publication.
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Additional info for A Student's Guide to the Mathematics of Astronomy
You still add exponents, taking care to retain the negative sign. Example: What is (3 × 103 ) × (2 × 10−10 )? (3 × 103 ) × (2 × 10−10 ) = (3 × 2) × (10(3+(−10)) ) = 6 × 103−10 = 6 × 10−7 . A similar approach works for dividing two numbers expressed in scientific notation, except that in this case you divide the coefficients and subtract the exponents. Example: What is (2 × 105 ) ÷ (4 × 103 )? 5 × 102 . 5 × 102 . 0 × 101 . When one of the exponents is negative, dividing works just the same. You still subtract exponents, taking care to retain the negative sign.
1 1 2 2 2 9 × 104 = 9 × 104 = 3 × (104 ) 2 = 3 × 10(4× 2 ) = 3 × 102 . √ 3 Example: What is 8 × 109 ? √ 1 1 3 3 3 8 × 109 = 8 × 109 = 2 × (109 ) 3 = 2 × 10(9× 3 ) = 2 × 103 . You may be able to do these in your head if the numbers are whole multiples of the root, such as the two examples above. Otherwise you’ll need a calculator. 24. 7 Calculator issues If you require precise answers and you’re allowed to use a calculator, be sure to enter numbers expressed in scientific notation into your calculator properly.
That’s because the “EXP” or “EE” button on scientific calculators means “times 10 to the power of”. So entering 6 EXP 24 or 6 EE 24 stores the number 6 times 10 to the power of 24 in the calculator. 0 is implicit. That is, 106 = 1 × 106 . To enter this in your calculator, type 1 EXP 6. Many students go astray and type 10 EXP 6, which is incorrect because it represents 10 × 106 , or 107 . 5 Chapter problems 39 If you’re thinking “I’ve always entered numbers by pressing the × button and then pressing 10 and ^, and I’ve been getting the right answers,” you should understand that this approach may give a correct or an incorrect answer depending on exactly which buttons you press before and after entering a number this way.