Prof. Andreoletti
LA NOTAZIONE SCIENTIFICA
Definizioni
Ricordiamo, a proposito delle potenze del 10, che 101 = 10
103 = 1.000
1012 = 1.000.000.000.000 ovvero 10n è uguale ad 1 seguito da n zeri.
Nel caso di potenze con esponente negativo ricordiamo che
0,01
100 1 10
10−2 = 12 = =
00001 ,
000 0 . 100
1 10
10−5 = 15 = =
ossia 10-n è uguale ad 1 diviso 1 seguito da n zeri, o più semplicemente 0 virgola n-1 zeri e 1 (in pratica 1 preceduto da n zeri e si conta anche lo zero che precede la virgola).
Ricordiamo inoltre le seguenti proprietà delle potenze (ci riferiamo solo alle potenze del 10 ma il discorso è generale)
10m·10n = 10m+n 10m:10n = 10m-n (10m)n = 10m·n
ESEMPI:
9 5 4 5
4 10 10 10
10 ⋅ = + = 107 ⋅10−3 =107+(−3) =107−3 =104
6 8
2 ) 8 ( 2 8
2 10 10 10 10
10 ⋅ − = +− = − = − 1012 :107 =1012−7 =105
10 3
7 ) 3 ( 7 3
7 :10 10 10 10
10 − = −− = + = 10−5 :103 =10−5−3 =10−8
20 5
4 5
4) 10 10
10
( = ⋅ = (10−7)3 =10−7⋅3 =10−21
28 )
7 ( 4 7
4) 10 10
10
( − − = − ⋅− =
Chiameremo ordine di grandezza di un numero, il valore della potenza del 10 più vicina a quel numero.
ESEMPI:
7,51·103 ordine di grandezza 104 4,81·102 " 102 6,81·10-17 " 10-16
ESERCIZI
1. Eseguire le seguenti operazioni con la calcolatrice:
(a) 3,2•104 + 1,34•105 (b) 5,6•10-24 + 2,3•10-22 (c) 7,4•1014 + 9,4•1015 (d) 8,2•10-32 + 7,6•10-33 (e) 4,2•10-4 - 1,4•10-5 (f) 7,53•1016 - 2,14•1014 (g) 8,7•1015 - 9,34•105 (h) 4,176•10-7 - 4,121•10-7
2. Scrivere in notazione scientifica i seguenti numeri:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
e 1.234.000.000.000( )
j 0,00000000000000340000123 ,
0 i
237 d
0000456 ,
0 h
000 . 000 . 000 . 000 . 000 . 780 . 1 c
00000012 ,
0 g
000 . 43 b
05 , 0 f
000 . 000 . 340 . 12 a
3. Scrivere per esteso (ovvero in notazione decimale) i seguenti numeri dati in notazione scientifica:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
21( )
224 12
12 17
7 3
2 5
10 4 , 3 j 10 5 , 4 e
10 23 , 1 i 10 5 , 6 d
10 62 , 5 h 10 56 , 2 c
10 7 , 4 g 10 2 , 3 b
10 51 , 2 f 10 34 , 1 a
−
−
−
−
−
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
4. Indicare l'ordine di grandezza dei seguenti numeri:
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( )
31( )
255 11
15 27
12 3
3 15
10 17 , 4 j 10
5 , 4 e
10 3 , 2 i 10 5 , 2 d
10 2 , 6 h 10 26 , 4 c
10 32 , 7 g 10
2 , 1 b
10 1 , 5 f 10
4 , 3 a
−
−
−
−
−
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
⋅
5. Eseguire le seguenti operazioni con la calcolatrice:
(a) 3,2•104 • 1,34•105 (b) 5,6•10-24 • 2,3•1022 (c) 7,4•1014 • 9,4•10-5 (d) 8,2•1032 • 7,6•10-29 (e) 4,2•10-4 : 1,4•10-5 (f) 7,53•1016 : 2,14•1014 (g) 8,7•1015 : 9,34•10-5 (h) 2,7•10-7 : 4,2•10-17
(a) 18
7,12 10⋅ − (b) 17
6,31 10⋅ −
22 20
17
4, 41 10 5,71 10 (c) 6,31 10
− −
−
⋅ + ⋅
⋅
15 14
18
7,18 10 5,13 10 (d) 7,12 10−
⋅ − ⋅
⋅
( )
11 34 32
11 2
6,67 10 6,34 10 5,80 10
(e) 1,5 10
⋅ − ⋅ ⋅ ⋅ ⋅
⋅
( )
11 34 32
11 2
6,67 10 4,31 10 7,11 10
(f) 2,15 10
⋅ − ⋅ ⋅ ⋅ ⋅
(
⋅ + ⋅)
+ ⋅ ⋅⋅
11 6 4
11
2,5 10 3 10 5,8 10
(g) 6 10
34 4 16
7 9
1, 44 10 4,31 10 2 10
(h) 4 10
2,5 10
⋅ − ⋅ − ⋅ − ⋅
⋅
[Risposte: (a) 4,44·102; (b) 6,13·1032; (c) 9,12·10-4; (d) 9,36·1032; (e) 1,09·1035; (f) 4,42·1034; (g) 5,93·10-6; (h) 0]
6 . Stabilire se le seguenti espressioni sono vere [V] o false [F]
a)
( )
108 −8 =100 [V] [F] f) 14 14 7 710 10 10 10
−
−
⋅ = [V] [F]
b) 1018−1016 =102 [V]
[F] g)
( )
100 0 =0 [V] [F]c)
−
−
− + =
3 3
6 3
10 10 10 1 10
[V]
[F] h) 10 : 100 3 −5 ⋅10−4 =0 [V] [F]
d) 3109 +10−12 =103 +10−4 [V] [F] i)
6 8
6 4
10 1 10
10 0
10
−
− ⋅
= [V] [F]
e) 310 109 ⋅ −12 =10 103⋅ −4 [V]
[F]
7. Calcolare il valore delle seguenti espressioni:
a)
(
4,9832 10⋅ −81+68000 10⋅ −88+0,00000001 10⋅ −75)(
8380000 10⋅ 75−58,8 10⋅ 80+0,025 10⋅ 83)
b)
( )
− − −
− − − −
⋅ + ⋅ − ⋅
− ⋅ − ⋅ + ⋅ − ⋅
51 54 48
5
8 12 8 6 3
8,7412 10 1436,8 10 0, 000178 10
0, 0911 10 23654 10 2, 0003 10 0, 00726 10
c)
(
14 9 22)
312 2
4 26 56
30
45002 10 200000 10 0, 00055 10 162000 10
306 10 10
0, 00027 10
−
−
⋅ − ⋅ + ⋅
⋅ − ⋅ +
⋅
d)
31 40 109
3 38 29 111
0,11609 10 90000 10 0, 06 10
234000 10 0, 000346 10 10
− − −
− − −
⋅ − ⋅ + ⋅
⋅ + ⋅
e)
( )( )
− − −
− − −
⋅ − ⋅ + ⋅
⋅ + ⋅ ⋅ + ⋅ + ⋅
26 32 30
9 11 6 44 51 53
8, 002 10 2500 10 10005 10
29, 08 10 92000 10 0, 00054 10 6600 10 1800000 10
f)
(
20 29 26)
294 83 93
3
0, 0004789 10 211800 10 232,9 10 8913000 10 0, 00005556 10 664300 10
− − −
− − −
⋅ − ⋅ + ⋅
⋅ − ⋅ + ⋅ [2,5·10-18]
g)
( )
78 65 74
48 40 46 37 3
0, 00000114 10 7300000 10 0, 0359 10
5981000 10− 0, 02681 10− 22000 10− 0, 000045 10−
⋅ − ⋅ + ⋅
⋅ − ⋅ + ⋅ − ⋅ [2·1099]
h) ⋅ − + ⋅ − − ⋅ − + ⋅ − − ⋅ −
⋅ − + ⋅ ⋅ − ⋅ − ⋅
41 49 28 35 37
6 5
15 17 23 19 25 27
0, 00063 10 33000 10 0, 00044 10 70000 10 2000000 10 80100 10 10 0, 0007 10 63300 10 0, 003 10 0,000433 10
i) ⋅ + ⋅ − ⋅
⋅ − + ⋅
51 45 52
44 50 54
0,14279 10 116060 10 0, 000285 10 810000 10 10 0, 000035 10
j)
38 36 41
51 47 52
10 0, 012 10 4800 10 2,38 10 800 10 0, 03 10
− − −
− + ⋅ + ⋅
⋅ − ⋅ − ⋅
