Ռացիոնալ թվեր

8.
ա) 352 = 3 * 10² + 5 * 10 + 2
բ) 5864 = 5 * 10³ + 8 * 10² + 6 * 10 + 4
գ) 60853 = 6 * 10⁴ + 8 * 10² + 5 * 10 + 3
դ) 80451 = 8 * 10⁴ + 4 * 10² + 5 * 10 + 1

9.
ա) 3 * 10³ + 2 * 10² + 1 * 10 = 3210
բ) 7 * 10⁴ + 4 * 10² + 5 * 10 + 9 = 70259
գ) 8 * 10⁵ + 2 * 10³ + 6 = 802006
դ) 5 * 10⁶ + 7 * 10⁴ + 2 * 10³ + 5 = 507205

10.
ա) 34,251 = 34 + 0,251
բ) 45 = 45 + 0
գ) -12,3 = -13 + 0,7
դ) -80,45 = -81 + 0,55

11.
ա) 45/4 = 11,25
բ) 37/40 = 0,925
գ) 127/25 = 5,08
դ) 99/50 = 1,98

12.
ա) 1,25 = 125/100 = 5/4
բ) 2,256 = 2256/1000 = 564/250
գ) 0,016 = 16/1000 = 4/250
դ) 3,625 = 3635/1000 = 29/8

13.
ա) 2/9 = 0,(2)
բ) 1/6 = 0,1(6)
գ) 22/7 = 3,(142857)
դ) 12/11 = 1,(09)

14.
ա) 5/12 և 0,42
5/12 = 0,41(6)
0,41(6) < 0,42
գ) 2/9 և 0,2
0,2 = 1/5
2/9 > 1/5

19.
ա) 0,(6) = 6/10 + 6/100 + …
b₁ = 6/10
q = 1/10
S = b₁/(1 – q) = 6/10 : 9/10 = 2/3

բ) 3,2(4) = 3,2 + 4/100 + 4/1000 + …
3,2 = 32/10 = 16/5
b₁ = 4/100
q = 1/10
S = b₁/(1 – q) = 4/100 : 9/10 = 4/90
16/5 + 4/90 = 292/90 = 146/45

գ) 0,0(25) = 25/1000 + 25/100000 + …
b₁ = 25/1000 = 1/40
q = 1/100
S = b₁/(1 – q) = 1/40 : 99/100 = 5/198

դ) 2,3(12) = 2,3 + 12/1000 + 12/100000 + …
2,3 = 23/10
b₁ = 12/1000 = 6/500
q = 1/100
S = b₁/(1 – q) = 6/500 : 99/100 = 2/165
23/10 + 2/165 = 763/330