Réponses

2014-03-25T11:51:11+01:00
Exercice 1
E = 2/5 + (-3/4) x 5
E = 2/5 + (-3x5/4)
E = 2/5 + (-15/4)
E = 2/5 - 15/4
E = 2x4/5x4 - 15x5/4x5
E = 8/20 - 75/20
E = -67/20

F = -(-1/5)² - 2/5
F = -(-1)²/(5)² - 2/5
F = -(1/25) - 2/5
F = -1/25 - 2x5/5x5
F = -1/25 - 10/25
F = -11/25

G = [4-(2-5)²]/(4+5)
G = [4-(-3)²]/9
G = (4-9)/9
G = -5/9

H = (3/2)² -(1/3) x(5/2)
H = (3x3/2x2) - (1x5/3x2)
H = 9/4 - 5/6
H = 9x3/4x3 - 5x2/6x2
H = 27/12 - 10/12
h = 17/12

Exercice 2
Rappel des calculs de puissance de 10 (^ se lit puissance)
10^0 = 1
10^1 = 10
10^a x 10^b = 10^(a+b)
1/10^a = 10^-a

a) C = (3,5x10^-11x2x10^8)/(0,2x10^-9)
C = (3,5x2x10^(-11+8))/(2x10^-1x10^-9)
C = (3,5x2x10^-3)/(2x10^(-1-9))
C = (3,5x2x10^-3)/(2x10^-10)
C = (3,5x10^-3x10^10x2)/2
C = 3,5x10^(-3+10)
C = 3,5 x 10^7

S = (2x10^-5x1,2x10^2)/(3x10^-7)
S = (2x1,2x10^(-5+2))x10^7/3
S = 2,4 x 10^(-3+7)/3
S = 0,8 x 10^4
S = 8 x 10^-1 x10^4
S = 8 x 10^(-1+4)
S = 8 x 10^3

b) C = 35000 x 10^3
donc S < C

c) C x S = 3,5 x 10^7 x 8 x 10^3
C x S = 3,5 x 8 x 10^(7+3)
C x S = 28 x 10^10
C x S = 280 000 000 000

C/S = (3,5 x 10^7)/(8 x 10^3)
C/S = (3,5 x 10^7 x 10^-3)/8
C/S = 0.4375 x 10^(7-3)
C/S = 0.4375 x 10^4
C/S = 4375

2014-03-25T12:43:12+01:00
Exercice 1
Ecrire les différentes étapes et donner le résultat sous forme de fraction simplifiée :

E = 2/5 + (-3/4) x 5
E = 2/5 - 3/4 x 5
E = 2/5 - 3 x 5
                 4
E = 2/5 - 12/4
E = 2 x 4 / 5 x 4 - 15 x 5 / 4 x 5
E = 8/20 - 75/20
E = - 67/20

F = - (-1/5)² - 2/5
F = - (-1)² / (5)² - 2/5
F = - (1/25) - 2/5
F = -1/25 - 2 x 5 / 5 x 5
F = -1/25 - 10/25
F = -11/25

G = 4 - (2 - 5)² / (4 + 5)
G = 4 - (-3)² / 9
G = (4 - 9) / 9
G = -5/9

H = (3/2)² - (1/3) x (5/2)
H = (3 x 3 / 2 x 2) - (1 x 5)
                             (3 x 2)
H = 9/4 - 5/6
H = 9 x 3 / 4 x 3 - 5 x 2 / 6 x 2
H = 27/12 - 10/12
H = 17/12

Exercice 2
Donner l'écriture scientifique de C et S

a)
C = (3,5 x 10⁻¹¹ x 2 x 10⁸) / (0,2 x 10⁻⁹)
C = (3,5 x 2 x 10)⁻¹¹⁺⁸ / (2 x 10⁻¹ x 10⁻⁹)
C = (3,5 x 2 x 10⁻³) / (2 x 10⁻¹⁻⁹)
C = (3,5 x 2 x10⁻³) / (2 x 10⁻¹⁰)
C = (3,5 x 10⁻³ x 10¹⁰ x 2) / 2
C = 3,5 x 10⁻³⁺¹⁰
C = 3,5 x 10⁷

S = (2 x 10⁻⁵ x 1,2 x 10²) / (3 x 10⁻⁷)
S = (2 x 1,2 x 10⁻⁵⁺²) x 10⁷ sur³
S = 2,4 x 10⁻³⁺⁷ / 3
S = 0,8 x 10⁴
S = 8 x 10⁻¹ x 10⁴
S = 8 x 10⁻¹⁺⁴
S = 8 x 10³

b) Comparer C et S :
C > S

c) Calculer le produit C x S et le quotient C/S
C x S = 3,5 x 10⁷ x 8 x 10³
C x S = 3,5 x 8 x 10⁷⁺³
C x S = 28 x 10¹⁰, soit  280 000 000 000


C/S = (3,5 x 10⁷) / (8 x 10³)
C/S = (3,5 x 10⁷ x 10⁻³) / 8
C/S = 0,4375 x 10⁷⁻³
C/S = 0,4375 x 10⁴
C/S = 4375