问题1.以标准形式表示以下数字
(i)6020000000000000
解决方案：
To express 6020000000000000 in standard form, first write it simply in the form of exponent
= 602 × 1013
There should be 1 digit before the decimal.
= 6.02 × 1015
The standard form is 6.02 × 1015
(ii)0.00000000000942
解决方案：
To express 0.00000000000942 in standard form, first write it simply in the form of exponent
= 942 × 10-14
There should be 1 digit before decimal.
The standard form is 9.42 × 10-12
(iii)0.00000000085
解决方案：
To express 0.00000000085 in standard form, first write it simply in the form of exponent
= 85 × 10-11
There should be 1 digit before decimal.
The standard form is 8.5 × 10-10
(iv)846×10 7
解决方案：
The standard form of decimal has to be expressed using 1 digit before the decimal.
= 8.46 × 102 × 107
= 8.46 × 102+7
= 8.46 × 109
The standard form is 8.46 × 109
(v)3759×10 -4
解决方案：
The standard form of decimal has to be expressed using 1 digit before the decimal.
= 3.759 × 103 × 10-4
= 3.759 × 103 + (-4)
= 3.759 × 10-1
The standard form is 3.759 × 10-1
(vi)0.00072984
解决方案：
To express 0.00072984 in standard form, first write it simply in the form of exponent
= 72984 × 10-8
There should be 1 digit before decimal.
The standard form is 7.2984 × 10-4
(vii)0.000437×10 4
解决方案：
To express 0.000437 × 104 in standard form, first write it simply in the form of exponent
= 437 × 10-6 × 104
= 437 × 10-2
= 4.37
The standard form is 4.37
(viii)4÷100000
解决方案：
= 4/100000
The standard form is 4 × 10-5
问题2.以通常的形式写下以下数字：
(i)4.83×10 7
解决方案：
Usual form is written after simple multiplication
4.83 × 10000000 = 48300000
The usual form is 48300000
(ii)3.02×10 -6
解决方案：
Usual form is written after simple multiplication
= 302 × 10-2 × 10-6
= 302 × 10-8
The usual form is 0.00000302
(iii)4.5×10 4
解决方案：
Usual form is written after simple multiplication
4.5 × 10000 = 45000
The usual form is 45000
(iv)3×10 -8
解决方案：
The power is -8, so the decimal should shift 8 places towards the left.
The usual form is 0.00000003
(v)1.0001×10 9
解决方案：
Usual form is written after simple multiplication
1.0001 × 1000000000 = 1000100000
The usual form is 1000100000
(vi)5.8×10 2
解决方案：
Usual form is written after simple multiplication
5.8 × 100 = 580
The usual form is 580
(vii)3.61492×10 6
解决方案：
Usual form is written after simple multiplication
3.61492 × 1000000 = 3614920
The usual form is 3614920
(vii)3.25×10 -7
解决方案：
Usual form is written after simple multiplication
= 325 × 10-2 × 10-7
= 325 × 10-9
The usual form is 0.000000325