F.4 Maths: Real numbers
2013-09-01 10:11 pm
1. Express 7.3333.. and 2.4545… in the form a/b, where a and b are intergers.2. Hence find the value of 7.333.*2.4545..
回答 (2)
2013-09-02 12:15 am
✔ 最佳答案
Q1. 7.3333
Let a be 7.3333,
10a = 73.3333
10a - a = 73.3333 - 7.3333
9a = 66
a = 22/3
2.4545
Let b = 2.4545
100b = 245.4545
100b - b = 245.4545 - 2.4545
99b = 243
b = 27/11
Q2.
7.333 * 2.4545
=22/3 * 27/11
=18
參考: myself
2013-09-02 12:00 am
Let n = 7.3333... (1)
10n = 73.3333... (2)
(2) - (1)
9n = 74
n = 74/9
Let m = 2.4545... (1)
100m = 245.4545... (2)
99m =243
m = 243 / 99 = 27 / 11
2.
(74 / 9) * (27 / 11)
= 222 / 11
10n = 73.3333... (2)
(2) - (1)
9n = 74
n = 74/9
Let m = 2.4545... (1)
100m = 245.4545... (2)
99m =243
m = 243 / 99 = 27 / 11
2.
(74 / 9) * (27 / 11)
= 222 / 11
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