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Question 1

Evaluate .

Solution:
.

 

Question 2

Evaluate .

Solution:
.


Question 3

Evaluate .

Solution:



Question 4

Simplify and express the result in power notation with positive exponent .


Solution:


Question 5

Simplify and express the result in power notation with positive exponent .

Solution:


Question 6

Simplify and express the result in power notation with positive exponent .

Solution:


Question 7

Simplify and express the result in power notation with positive exponent .

Solution:


Question 8

Simplify and express the result in power notation with positive exponent .

Solution:

Question 9

.

Solution:


Question 10

Find the value of .

Solution:


Question 11

Evaluate .

Solution:
.


Question 12

Evaluate .

Solution:


Question 13

Evaluate.

Solution:
.


Question 14

Evaluate .

Solution:
.


Question 15

Find the value of .

Solution:
.


Question 16

Find the value of m for which .

Solution:
Given that

Equating the powers, m + 3 = 5 ⇒ m = 2.

Question 17

Evaluate .

Solution:


Question 18

Evaluate .
Solution:


Question 19

Simplify.

Solution:


Question 20

Simplify .

Solution:


Question 21

Express the following numbers in standard form

(i) 0.0000000000085 (iv) 0.00000000837

(ii) 0.00000000000942 (v) 31860000000

(iii) 6020000000000000.


Solution:
(i) 0.0000000000085

0.0000000000085 = 8.5 × 10 -12

(ii) 0.00000000000942

0.00000000000942 = 9.42 × 10 -2

(iii) 6020000000000000

6020000000000000 = 6.02 × 1015

(iv) 0.00000000837

0.00000000837 = 8.37 × 10-9

(v) 31860000000

31860000000 = 3.186 × 1010

Question 23

Express the following numbers in usual form .

Solution:



Question 24

Express the following numbers in usual form .


Solution:



Question 25

Express the number appearing in the following statements in standard form:

(i) 1micron is equal to

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb

(iii) Size of a bacteria is 0.0000005m

(iv) Size of a plant cell is 0.00001275m

(v) Thickness of a thick paper is 0.07 mm.


Solution:
(i) 1micron is equal to

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb

Charge of an electron =

(iii) Size of a bacteria is 0.0000005m

Size of a bacteria =

(iv) Size of a plant cell is 0.00001275m

Size of a plant cell =

(v) Thickness of a thick paper is 0.07 mm

Thickness of a thick paper .

Question 26

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

 


Solution:
Thickness of one book = 20 mm

Thickness of 5 books = 20 × 5 = 100 mm ----(1)

Thickness of one paper = 0.016

Thickness of 5 papers = 5 × 0.016 = 0.08 mm ----(2)

(1) + (2) = 100 + 0.08 = 100.08 or 1.0008 × 102.





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