1. To complete a job alone, A needs 12 days, B needs 18 days and C needs 24 days. Now , the job is carried out by A first for several days, and then by B for several days, and finally completed by C. The ratios of their working days are A:B = 1:3 and B:C = 1:2.
Find the total number of working days for completing the job.
For questions 2 and 3, how many zeros are there in the valu of each of the
following expressions?
2. (10^7)^10
3. 15^2010 X 6^2009 X5^2008
4. Write the following expression as binary numbers
1 X 4 + 1 X 1 + 1 X (1/2)
5. Use the digits 0,0,1,2,3 to form a number which must be correct to 5 significant figures.
A. 0.0123
B. 0.1230
C. 1.0230
D. 12300
With expanation please.
F.2 Maths
2013-12-30 12:04 am
回答 (1)
2013-12-30 7:18 am
✔ 最佳答案
(1)In 1 day.
A can finish 1/12 of the job.
B can finish 1/18 of the job.
A can finish 1/24 of the job.
Let
A works for a days.
B works for b days.
C works for c days.
A finish a/12 of the job.
B finish b/18 of the job.
C finish c/24 of the job.
a/12 + b/18 + c/24 = 1 .... (1)
a/b = 1/3 ; 3a = b ..... (2)
b/c = 1/2 ; c = 2b ; c = 6a .... (3)
sub. (2) and (3) into (1)
a/12 + 3a/18 + 6a/24 = 1
(6a+12a+18a)/72 = 1
36a = 2
a = 2
b = 6
c = 12
Total number of working days = 2+6+12 = 20 days
(2)
(10⁷)¹⁰ = 1× 10⁷⁰ ; 70 zeros
(3)
15²⁰¹⁰ × 6²⁰⁰⁹ × 5²⁰⁰⁸
= 3²⁰¹⁰ × 5²⁰¹⁰ × 2²⁰⁰⁹ × 3²⁰⁰⁹ × 5²⁰⁰⁸
= 3²⁰¹⁰⁺²⁰⁰⁹ × 5²⁰¹⁰⁺²⁰⁰⁸ × 2²⁰⁰⁹
= 3⁴⁰¹⁹ × 5⁴⁰¹⁸ × 2²⁰⁰⁹
= 3⁴⁰¹⁹ × 2²⁰⁰⁹ × 5²⁰⁰⁹ × 5²⁰⁰⁹
= 3⁴⁰¹⁹ × 5²⁰⁰⁹ × 2²⁰⁰⁹ × 5²⁰⁰⁹
= 3⁴⁰¹⁹ × 5²⁰⁰⁹ × 10²⁰⁰⁹
There are 2009 zeros
(4) 101.1
....... (128) (64) (32) (16) (8) (4) (2) (1) . (1/2) (1/4) (1/8) .......
therefore 101.1(2)
5. The answer is C
A is 4 sig. fig
B is 4 sig. fig
C is 5 sig. fig
D is 3 sig. fig
if D written as 1.2300 × 10⁴ ; then it is 5 sig. fig
2013-12-29 23:56:40 補充：
5A is 3 sig. fig
收錄日期: 2021-04-27 20:35:23
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