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Chapter 2 of RD Sharma's Class 8 Mathematics textbook delves into the concept of Powers, with Exercise 2.3 focusing specifically on the laws of exponents and their applications to more complex scenarios.
This exercise builds upon the fundamental principles introduced in earlier sections, challenging students to apply their knowledge to a wider range of problems.
(i) 6020000000000000
Solution:
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
Solution:
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
Solution:
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 × 107
Solution:
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
Solution:
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
Solution:
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 × 104
Solution:
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
Solution:
= 4/100000
The standard form is 4 × 10-5
(i) 4.83 × 107
Solution:
Usual form is written after simple multiplication
4.83 × 10000000 = 48300000
The usual form is 48300000
(ii) 3.02 × 10-6
Solution:
Usual form is written after simple multiplication
= 302 × 10-2 × 10-6
= 302 × 10-8
The usual form is 0.00000302
(iii) 4.5 × 104
Solution:
Usual form is written after simple multiplication
4.5 × 10000 = 45000
The usual form is 45000
(iv) 3 × 10-8
Solution:
The power is -8, so the decimal should shift 8 places towards the left.
The usual form is 0.00000003
(v) 1.0001 × 109
Solution:
Usual form is written after simple multiplication
1.0001 × 1000000000 = 1000100000
The usual form is 1000100000
(vi) 5.8 × 102
Solution:
Usual form is written after simple multiplication
5.8 × 100 = 580
The usual form is 580
(vii) 3.61492 × 106
Solution:
Usual form is written after simple multiplication
3.61492 × 1000000 = 3614920
The usual form is 3614920
(vii) 3.25 × 10-7
Solution:
Usual form is written after simple multiplication
= 325 × 10-2 × 10-7
= 325 × 10-9
The usual form is 0.000000325
Exercise 2.3 of Chapter 2 in RD Sharma's Class 8 Mathematics textbook provides an in-depth exploration of advanced exponent operations and their applications. This exercise challenges students to apply the laws of exponents to more complex scenarios, including expressions with multiple bases, fractional and negative exponents, and equations involving powers. Through a carefully curated set of problems, students learn to simplify intricate expressions, solve equations with variables in exponents, and work with powers of fractions and decimals. The exercise emphasizes the importance of systematic problem-solving and encourages students to develop strategies for tackling complex mathematical expressions. By mastering these concepts, students build a strong foundation for more advanced topics in algebra, calculus, and other areas of mathematics, while also honing their analytical and logical reasoning skills.
