Indices and standard form
Embed Size (px)
Transcript of Indices and standard form
- 1. Slide 1 01Chapter Indices and Standard Form Earth to Sun: 144 000 000 kmEarth to Moon: 384 835 kmWhat about the distance from the Earth to the Moon?We know that the Sun is very far from the Earth.But how far exactly is it?How many digits are needed to represent this distance?Its 144 000 000 km,or 1.440 00 x 100 000 000 km,or 1.440 00 x 108 km.
2. Slide 2 01Chapter Indices and Standard FormEarth:6.6 x 1021 metric tonsSun:22 x 1027 metric tonsMoon:7.3 x 1019 metric tonsBesides the distances mentioned earlier, even the masses of theEarth, the Moon and the Sun are pretty large too.The numbers involved are so large that we make use ofINDICES to represent them. 3. Slide 3 01ChapterIndices and Standard FormBesides representing very large numbers, we can also makeuse of INDICES to represent very small numbers.Some examples: diameter of a strand of hair, size ofan atom, size of a bacterium Diameter of a human hair: 0.000 025 4 m We can rewrite it as 25.4 x 0.000 001 m,or 25.4 x 10-6 mWhat are INDICES then? 4. Slide 4 01ChapterIndices and Standard Form 1.440 00 x 108 km 25.4 x 10-6 mThese numbers are called INDICES.We make use of INDICES to represent extremelyLARGE or small numbers.INDICES saves us from writing long string ofdigits, saving time and effort, and reducing thechance of missing out digits. 5. Slide 5 01Chapter Indices and Standard FormImagine having to write out 22 x 1027 which is thevalue of the mass of the Sun, in full in yourassignment about the Solar System. 22 x10 27= 22 000 000 000 000 000 000 000 000 6. Slide 6 01ChapterIndices and Standard Form2 x 2 x 2 can be written as 23,where23 Index / ExponentBase 7. Slide 7 01ChapterIndices and Standard Formam35= a xx aa x xa a x a x a a m times 8. Slide 8 01ChapterIndices and Standard FormBelow are the laws of indices for expressions with a commonbase. a xa = a m n m+n a a =am nm-n(a ) = am nm n 9. Slide 9 01Chapter Indices and Standard FormSummarya xa = am nm+na a =a mnmn(a ) = a = am nm nmn 10. Slide 10 01ChapterIndices and Standard FormBelow are the laws of indices for expressions with a commonindex. a3 b3 x= (a (a) (a) x b) (b) (b)(a) (a (a (b) b) b)= 3= (a b) 11. Slide 11 01ChapterIndices and Standard Forma 3 (a) (a) (a) a a3=b (b) (b) (b) b b3 a a a= b b b 12. Slide 12 01ChapterIndices and Standard FormSummarya x b = (ab) m mmama b = ( b) mm 13. Slide 13 01ChapterIndices and Standard Forma = 10 Zero Index- =-31a2n8 n3Negative Indexa2 12 n3284a = a 3 n842 Fractional Index 14. Slide 14 01ChapterIndices and Standard FormMore on Fractional Index 13 n38a n= a82m1nn ma = a2133 28 = 4 64 8 15. Slide 15 01ChapterIndices and Standard FormSummarya =1 01 a = an -n1n mna n = a a n = am 16. Slide 16 01ChapterIndices and Standard FormEquations Involving Indices4 x=164 2 x = 2 17. Slide 17 01ChapterIndices and Standard FormIndex Earth to Sun:(plural: indices) 8 1.440 00 x 10 kmThen what is this form ofexpressing numbers known as?1.440 00 x 108 standard form of 144 000 000A, where 1 A < 10 nn is an integer. In general, A x 10 18. Slide 18 01ChapterIndices and Standard Form Standard form for very large numbers144 000 000 8 6 3Numbers larger than 1,move to the leftIs 1 A < 10 now?Yes! So, in standard form:1.440 00 x 108 19. Slide 19 01Chapter Indices and Standard Form Standard form for very small numbersNumbers smaller than 1,move to the right.0.000 000 14436 7 Is 1 A < 10 now? Yes! So, in standard form:-7 1.440 00 x 10