Standard Form

Significant figures 1). 4357 2) 43.57 3) 70.4 4) 1.0003 5) 19.10 6) 70.30 7) 8000.300 8) 5000 9) 5690000

a. 0.3 B. 0.102 C. 0.20200 D. 0.000303 E. 0.000045005 F. 0.00062500

Topic 1: Standard Form

Learning Objectives :

Learning Outcome :

1.2 Understand and use the concept of standard form to solve problems

iii At the end of the lesson, the students should able to perform operations of addition and subtraction involving any two numbers and state the answers in standard form.

Example 1:

2.4 x 103 + 1.5 x 102

= 2.4 x 103 + 0.15 x 103

= (2.4 + 0.15) x 103

= 2.55 x 103

Become bigger,

that is 3

Become smaller,

that is 0.15

Example 2:

5.6 x 10-7 – 4.2 x 10-8

= 5.6 x 10-7 - 0.42 x 10-7

= (5.6 - 0.42) x 10-7

= 5.18 x 10-7

Become bigger,

that is -7

Become smaller,

that is 0.42

Example 3:

3.4 x 103 + 800

= (3.4 + 0.8) x 103

= 4.2 x 103

Become bigger,

that is 3

Become smaller,

that is 0.8

= 3.4 x 103 + 8.0 x 102

= 3.4 x 103 + 0.8 x 103

Example 4:

= (0.45 + 2.5) x 10-3

= 2.95 x 10-3

Become bigger,

that is -3

Become smaller,

that is 0.45

= 4.5 x 10-4 + 2.5 x 10-3

= 0.45 x 10-3 + 2.5 x 10-3

0.00045 + 2.5 x 10-3

Example 5:

6.2 x 105 – 3 x 104

= 6.2 x 105 - 0.3 x 105

= (6.2 - 0.3) x 105

= 5.9 x 105

Become bigger,

that is 5

Become smaller,

that is 0.3

Example 6:

= (9.9 – 0.18) x 105

= 9.72 x 105

Become bigger,

that is 5

Become smaller,

that is 0.18

= 9.9 x 105 – 1.8 x 104

= 9.9 x 105 – 0.18 x 105

990000 – 1.8 x 104

Become smaller,

that is 0.123

Example 7:

= (9.879 – 0.123) x 10-2

= 9.756 x 10-2

Become bigger,

that is -2

= 9.879 x 10-2 – 1.23 x 10-3

= 9.879 x 10-2 – 0.123 x 10-2

9.879 x 10-2 – 0.00123

Work sheet : Evaluate the following and give your answer in standard form

1 6.32 x 105 + 3.22 x 104 6.642 x 105

2 5.58 x 108 -2.84 x 107 5.296 x 108

3 4.6 x 10-4 - 3.3 x 10-5 4.27 x 10-4

4 2.01 x 10-4 + 3.75 x 10-5 2.385 x 10-4

Work sheet : Evaluate the following and give your answer in standard form

5 72 000 + 3.6 x 105 4.32 x 105

6 8.5 x 106 – 570 000 7.93 x 106

7 0.040021 – 0.005461 3.456 x 10-2

am x an = am+n

am ÷ an = am―n

Answer : Indices Theorem

Examples :

1. 32 x 33 =

2. 25 ÷ 23 =

3. 46 x 47 =

4. m5 ÷ m3 =

5. 2b4 x 3b5 =

35

22

413

m2

6b9

Examples :

420000 x 0.006 = ?

How to solve it ?

420000 ÷ 0.006 = ?

Step 1 : Change the numbers to Standard form.

420000 x 0.006 = 4.2 x 105 x 6 x 10-3 Step 2 : Multiply the numbers and add the

power numbers.

4.2 x 105 x 6 x 10-3 = 4.2 x 6 x 105+ (-3)

= 25.2 x 102

Answer = 2.52 x 103

Step 3 : Change the answer to Standard form.

Examples 1 : 420000 x 0.006 = ?

Examples 2 : 420000 ÷ 0.006 = ?

Step 1 : Change the numbers to Standard form.

420000 ÷ 0.006 = 4.2 x 105 ÷ 6 x 10-3 Step 2 : Divide the numbers and subtract

the power numbers.

4.2 x 105 ÷ 6 x 10-3 = 4.2 ÷ 6 x 105- (-3)

= 0.7 x 108

Answer = 7 x 107

Step 3 : Change the answer to Standard form.

Step 1 : Change the numbers to Standard form.

Step 2 : Multiply the numbers and add the power numbers.

6.8 x 10-2 x 9 x 106 = 6.8 x 9 x 10-2+6

= 61.2 x 104

Answer = 6.12 x 105

Step 3 : Change the answer to Standard form.

Examples 3 : 6.8 x 10-2 x 9 x 106 = ?

Examples 4 : 3.9 x 10-7 ÷ 3.0 x 104 = ?

Step 1 : Change the numbers to Standard form.

Step 2 : Divide the numbers and subtract the power numbers.

3.9 x 10-7 ÷ 3.0 x 104 = ( 3.9 ÷ 3.0 ) x 10-7- (4)

= 1.3 x 10-11

Answer = 1.3 x 10-11

Step 3 : Change the answer to Standard form.

Exercise

1. 8.9 x 5 x 107 =

2. 6.4 x 1011 ÷ 8.0 x 10-5 =

3. 36 x 10-6 x 4 x 10-5 =

4. 63000 ÷ 7 x 106 =

5. 0.0048 ÷ 6000 =

4.45 x 108

8 x 1015

9 x 10-11

9 x 10-3

8 x 10-7

Using The Scientific Calculator

Examples :2.75 x 107 x 7.24 x 108

Press

2 . 75 Exp 7 X 7 . 2 4 Exp 8 =

Let’s try !

3. 6.5 x 10-6 x 4.8 x 10-7

1. 8.5 x 10-2 ÷ 5 x 10-4

2. 5.5 x 104 ÷ 5 x 108

ExerciseSolve each of the following and state the answer in standard form.

1. 0.064 x 9400

2. 0.051 ÷ 3000

3. 3.4 x 109 x 2 x 10-5

4. 8.4 x 10-7 ÷ 4 x 10-4

5. 360000 ÷ ( 9 x 5 x 10-2 )