问题1.以标准形式表示以下数字:
(i)0.0000000000085
(ii)0.00000000000942
(iii)6020000000000000
(iv)0.00000000837
(v)31860000000
解决方案:
(i) 0.0000000000085
= 85/10000000000000 = 85/1013 = 85 × 10-13
= 8.5 × 10 × 10-13 = 8.5 × 101-13 = 8.5 × 10-12
So, the required standard form is 8.5 × 10-12
(ii) 0.00000000000942
= 942/100000000000000 = 942/1014 = 942 × 10-14
= 9.42 × 102 × 10-14 = 9.42 × 102-14 = 9.42 × 10-12
So, the required standard form is 9.42 × 10-12
(iii) 6020000000000000
= 602 × 10000000000000
= 6.02 × 102 × 1013 = 6.02 × 1015
So, the required standard form is 6.02 × 1015
(iv) 0.00000000837
= 837/100000000000 = 837/1011 = 837 × 10-11
= 8.37 × 102 × 10-11 = 8.37 ×102-11 = 8.37 × 10-9
So, the required standard form is 8.37 × 10-9
(v) 31860000000
= 3186 × 10000000
= 3.186 × 103 × 107 = 3.186 × 1010
So, the required standard form is 3.186 × 1010
问题2.以通常的形式表示以下数字
(i)3.02×10 -6
(ii)4.5×10 4
(iii)3×10 -8
(iv)1.0001×10 9
(v)5.8×10 12
(六)3.61492×10 6
解决方案:
(i) 3.02 × 10-6
= 3.02/106
= 302 × 1/102 × 1/106 = 302/102+6
= 302/108 = 0.00000302
So, the usual form is 0.00000302
(ii) 4.5 × 104
= 45/101 × 104
= 45 × 10-1 × 104 = 45 × 10-1+4
= 45 × 103 = 45000
So, the usual form is 45000
(iii) 3 × 10-8
= 3/108
= 3/100000000 = 0.00000003
So, the usual form is 0.00000003
(iv) 1.0001 × 109
= 10001/10000 × 109
= 10001 × 10-4 × 109 = 10001 × 10-4+9
= 10001 × 105 = 1000100000
So, the usual form is 1000100000
(v) 5.8 × 1012
= 58 X 10-1 × 1012
= 58 × 10-1+12 = 58 × 1011
= 5800000000000
So, the usual form is 5800000000000
(vi) 3.61492 × 106
= 361492/100000 × 106
= 361492 × 10-5 ×106 = 361492 × 10-5+6
= 3614920
So, the usual form is 3614920
问题3.以标准形式表示以下语句中出现的数字。
(i)1微米等于1/1000000 m。
(ii)电子的电荷为0.000,000,000,000,000,000,16库仑
(iii)细菌大小为0.0000005 m
(iv)植物室的大小为0.00001275 m
(v)厚纸的厚度为0.07毫米。
解决方案:
(i) 1 micron = 1/1000000 m
= 1/106 = 10-6 m
So, the standard from is 10-6 m
(ii) Charge of an electron = 0.000,000,000,000,000,000,16 C
= 16/100000000000000000000 = 16/1020 = 1.6 × 10 X10-20
= 1.6 × 101-20 = 1.6 × 10-19
So, the standard from is 1.6 × 10-19 C
(iii) Size of Bacteria = 0.0000005 m
= 5/10000000 = 5/107 = 0.5 × 10 × 10-7
= 0.5 × 10-6
So, the standard from is 0.5 × 10-6 m
(iv) Size of plant cell = 0.00001275 m
= 1275/100000000 = 1275/108 = 1.275 × 103 × 10-8
= 1.275 × 103-8 = 1.275 × 10-5
So, the standard from is 1.275 × 10-5 m
(v) Thickness of a Paper = 0.07mm
= 7/100 = 7/102 = 0.7 × 10 × 10-2
= 0.7 × 10-1
So, the standard from is 0.7 × 10-1 mm
问题4.在一堆中,有5本书,每本的厚度为20毫米,每本有5张纸,每本的厚度为0.016毫米。堆叠的总厚度是多少?
解决方案:
The thickness of Books will be 5 × 20mm = 100mm or 10cm
The thickness of Paper sheets will be 5 × 0.016mm = 0.080mm
Hence, the total thickness is = thickness of books + thickness of paper sheets
= 100mm + 0.080mm = 100.080mm
or
1.0008 × 10-2 mm