By Arthur J. Lyon and W. Ashhurst (Auth.)
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4. 5. (a) +10%. (b) +0-1%. (c)+2%. (a) ±2g. (b) +8g. (c) +0-04 g. (a) + 5 V . (b) +0-01 V. (a) 12-5 + 0-1. (b) + 0-8%. (c) +0-8%. (d) + 3 Ω. (a) 5%. (b) No. (c) 5%. (d) 5%. (e) No. (f) 10%. (g) 10%. (h) 2 | % . (i) 2 1 % . (j) 15%. (k) No. (1) 2 1 % . (m) No. (n) 7 | % . 6. (a) 5. (b) 0-5. (c) 0-05. (d) 0-5. (e) No. (f) No. (g) 1*5. 7. (a) 40-0+1-2. (b) 400+24 (6%). (c) 0-0500 + 0-0015 (3%). (d) 2-00+0-03(11%). (e) 300+0-6. (f) 00333 + 00007 (2%). (g) 100+0-6. (h) 0-100+0-006 (6%). (i) 1000+180 (18%).
Are Ex9 Ey, Ez, . . , and if these are small compared with the values x,y9z, . . 7) It is worth noting that when dealing with a trigonometric function an angular error estimate given in degrees must be converted to radians (r) if the usual differentiation formulae are used. For example, if u = sin Θ, ou = cos Θ <50, where δθ is in radians. 5 Calculate u and its maximum error if u = ex sin y, where x = 2-75 + 0-02 and y = 48°20 / ±10 / . From four-figure tables, e2"75 = 15-64 and sin 48°20' = 0-7470, and using logarithm tables gives the product as u = 11-68.
1, the number of significant figures is a rather poor guide to relative accuracy; for example, a number correct to three significant figures can have any accuracy between ±0-05% and ±0-5%, depending on its initial digit. It is therefore not possible to state as simple rules for generalized products as for generalized sums. e. (fc + 1), (fc+2), or(fc+3) significant figures altogether. (a) Before discussing this further, let us return to the gross mistakes given at the beginning of the section. In the first one the student apparently felt thatfiguresbeyond the third decimal place were negligible and to be discarded, and therefore rounded 0-00462 to 0-005.