Standard Form
Transcript of 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 )