Answer
0.32
Step-by-step explanation:
"0.2222" was replaced by "(2222/10000)". 4 more similar replacement(s)
1111
Simplify ————
5000
22 222 2 1111
(((———•4)•{————}3——)•5)•(————2)
100 1000 10 5000
1111 = 11•101
(1111)2 = (11•101)2 = 112 • 1012 2.2 5000 = 23•54 (5000)2 = (23•54)2 = 26 • 58
22 ( 222 2 (112•1012)
(((———•4)•{————}3——)•5)•——————————
100 1000 10 (26•58)
1
Simplify —
5
22 ( 222 1 (112•1012)
(((———•4)•{————}3—)•5)•——————————
100 1000 5 (26•58)
111
Simplify ———
500
22 111 1 (112•1012)
(((———•4)•———3)—)•5)•——————————
100 500 5 (26•58)
5.1 111 = 3•37
(111)3 = (3•37)3 = 33 • 373 5.2 500 = 22•53 (500)3 = (22•53)3 = 26 • 59
22 (33•373) 1 (112•1012)
(((———•4)•———————— ÷ —)•5)•——————————
100 (26•59) 5 (26•58)
(33•373) 1
Divide ———————— by —
(26•59) 5
6.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
(33•373) 1 (33•373) 5
———————— ÷ — = ———————— • —
(26•59) 5 (26•59) 1
Dividing exponents:
6.2 51 divided by 59 = 5(1 - 9) = 5(-8) = 1/58
22 (33•373) (112•1012)
(((——— • 4) • ————————) • 5) • ——————————
100 (26•58) (26•58)
11
Simplify ——
50
11 (33•373) (112•1012)
(((—— • 4) • ————————) • 5) • ——————————
50 (26•58) (26•58)
Multiplying exponents
8.1 52 multiplied by 58 = 5(2 + 8) = 510
Dividing exponents:
8.2 21 divided by 26 = 2(1 - 6) = 2(-5) = 1/25
Equation at the end of step
8
:
(11•33•373) (112•1012)
(——————————— • 5) • ——————————
(510•25) (26•58)
Dividing exponents
9.1 51 divided by 510 = 5(1 - 10) = 5(-9) = 1/59
(11•33•373) (112•1012)
——————————— • ——————————
(59•25) (26•58)
Multiplying exponents
10.1 111 multiplied by 112 = 11(1 + 2) = 113
Multiplying exponents:
10.2 59 multiplied by 58 = 5(9 + 8) = 517
Multiplying exponents:
10.3 25 multiplied by 26 = 2(5 + 6) = 211
Final result :
(113•33•373•1012)
————————— = 0.32
(517•211)
