问题1：以p / q格式表示以下每个小数：
(i)0.39
(ii)0.750
(iii)2.15
(iv)7.010
(v)9.90
(vi)1.0001
解决方案：
(i) Multiplying and Dividing the number by 100
0.39 = 39/100
(ii) Multiplying and Dividing the number by 1000
0.750 = 750/1000 = 3/4
(iii) Multiplying and Dividing the number by 100
2.15 = 215/100 = 43/20
(iv) Multiplying and Dividing the number by 1000
7.010 = 7010/1000 = 701/100
(v) Multiplying and Dividing the number by 100
9.90 = 990/100 = 99/10
(vi) Multiplying and Dividing the number by 10000
1.0001 = 10001/10000
问题2：以p / q格式表示以下每个小数：
解决方案：
(i) Let x = 0.4̅
or x = 0.4̅ = 0.444 …. (1)
Multiplying both sides by 10
10x = 4.444 …..(2)
Subtract (1) by (2), we get
10x – x = 4.444… – 0.444…
9x = 4
x = 4/9
=> 0.4̅ = 4.9
(ii) Let x = 0.3737.. …. (1)
Multiplying both sides by 100
100x = 37.37… …..(2)
Subtract (1) from (2), we get
100x – x = 37.37… – 0.3737…
100x – x = 37
99x = 37
x = 37/99
(iii) Let x = 0.5454… (1)
Multiplying both sides by 100
100x = 54.5454…. (2)
Subtract (1) from (2), we get
100x – x = 54.5454…. – 0.5454….
99x = 54
x = 54/99
(iv) Let x = 0.621621… (1)
Multiplying both sides by 1000
1000x = 621.621621…. (2)
Subtract (1) from (2), we get
1000x – x = 621.621621…. – 0.621621….
999x = 621
x = 621/999
or x = 23/37
(v) Let x = 125.3333…. (1)
Multiplying both sides by 10
10x = 1253.3333…. (2)
Subtract (1) from (2), we get
10x – x = 1253.3333…. – 125.3333….
9x = 1128
or x = 1128/9
or x = 376/3
(vi) Let x = 4.7777…. (1)
Multiplying both sides by 10
10x = 47.7777…. (2)
Subtract (1) from (2), we get
10x – x = 47.7777…. – 4.7777….
9x = 43
x = 43/9
(vii) Let x = 0.47777….
Multiplying both sides by 10
10x = 4.7777…. …(1)
Multiplying both sides by 100
100x = 47.7777…. (2)
Subtract (1) from (2), we get
100x – 10x = 47.7777…. – 4.7777…
90x = 43
x = 43/90