Exercise 4.2

1. Express the following numbers in standard form:

i. 0.000000000947

Solution:

x 10−1010−9

ii. 543000000000

Solution:

x 1011109

iii. 48300000

Solution:

x 107106

iv. 0.00009298

Solution:

x 10−510−6

v. 0.0000529

Solution:

x 10−510−4

2. Express the following numbers in usual form:

i. 4.37 × 105

Solution:

ii. 5.8 × 105

Solution:

iii. 32.5 × 105

Solution:

iv. 3.71529 × 105

Solution:

v. 3789 × 105

Solution:

vi. 24.36 × 105

Solution:

3. Express the following information in standard form

i. Size of the bacteria is 0.0000004 m

Solution:

4 x 10−710−6 m

ii. The size of red blood cells is 0.000007mm

Solution:

7 x 10−610−4 mm

iii. The speed of light is 300000000 m/sec

Solution:

3 x 10⁸ m/sec

iv. The distance between the moon and the earth is 384467000 m(app)

Solution:

3.84467 x 108106 m

v. The charge of an electron is 0.00000000000000000016 coulombs

Solution:

1.6 x 10151011 coulombs

vi. The charge of an electron is 0.00000000000000000016 coulombs

Solution:

1.6 x 10−1910−17 coulombs

vii. The charge of an electron is 0.00000000000000000016 coulombs

Solution:

1.6 x 10−1910−16 coulombs

4. In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the pack.

Solution:

Thickness of 5 books = 5 × 20 mm = mm

Thickness of 5 paper sheets = 5 × 0.016 mm = mm

Total thickness of the pack = Thickness of books + Thickness of paper sheets

= 100 mm + 0.08 mm

= mm

Therefore, the total thickness of the pack is mm.

5. Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why ? Justify your argument.

i. x−3×x−2 = x−6

Solution:

NoYes, I agree with Rakesh's solution.

The correct solution is:

x−3 × x−2 = x−3+−2 = x−5 (Reason: When multiplying exponents with the same base, we the powers.)

Rakesh incorrectly multiplied the exponents instead of adding them. The correct answer is x−5, not x−6.

ii. x3x2 = x4

Solution:

I agree with Rakesh's solution: NoYes

The correct solution is:

x3x2 = x3−2 = (Reason: When dividing exponents with the same base, we the powers.)

Rakesh incorrectly added the exponents instead of subtracting them. The correct answer is x, not x⁴.

iii. x23 = x23 = x8

Solution:

I agree with Rakesh's solution: NoYes

The correct solution is:

(x²)³ = x2×3 = x6x5

Rakesh made two mistakes:

First, he wrote x23 which implies x to the power of . This isn't what the original expression means.

Secondly, he seems to have solved the exponents like: 23 to get 8. He should have multiplied them. The correct answer is x6, not x8.

iv. x−2 = x

Solution:

I agree with Rakesh's solution: YesNo

The correct interpretation of x−2 is:

x−2 = 1x2xx2 (Reason: A negative exponent means you take the reciprocal of the base raised to the positive version of that exponent.)

The square root of x (x) can be written as x12x2. These are not equivalent to x−2.

v. 3x−1 = 13x

Solution:

I agree with Rakesh's solution: YesNo

The correct solution is:

3x−1 = 3 × () = (Reason: Only the term with the negative exponent is affected by it. The constant 3 is not raised to the power of -1.)

Rakesh incorrectly applied the exponent to the constant as well. The correct answer is 3x, not 13x.