Standard Form
Objectives:
B Grade
Use standard index form with and without a
calculator
Prior knowledge:
Understand :
Positive index laws
Simplifying fractions and dividing with decimals
Standard Form
Standard form is used for writing either very large numbers or
very small numbers by showing how many times that a
single digit number would be either multiplied or divided by 10
Standard form is written in the form
#.# ×
10x
an integer between 1 and 9
Example 1:
the power of 10
an integer between 1 and 9
700 can be written as 7 × 100
100 is 10 × 10 or 102
So now 700 can be written as 7 × 102
Standard Form
Example 2:
1400 can be written as 1.4 × 1000
1000 is 10 × 10 × 10 or 103
so now 1400 can be written as 1.4 × 103
To help understand this think of the place value
Example 3:
0.0005
1
10 000
can be written as 5 ×
Using negative index laws
1
is
1
10 000
10 × 10 × 10 × 10
1
10 000
or 10-4
so now 0.0005 can be written as 5 × 10-4
Standard Form
Now do these:
Write these numbers in standard form:
1.
4000 4 × 104 2.
500 5 × 102
4.
46 000
46 4.6 × 101 6.
5.
7.
4.6 × 104
0.007 7 × 10 3 8.
10.
0.421
11.
4.21 × 10
-1
3.
-
70000 7 × 104
2560 2.56 × 103
3.5 × 10-3
0.0004 4 × 10 4 9.
0.0035
0.000055
19 million
-5
5.5 × 10
12.
1.9 × 107
13. Avogadro’s number is 602 300 000 000 000 000 000 000. Express this
in standard form.
23
6.023 × 10
14.
A certain virus is 0.000 000 000 25 cm in diameter. Express this
in standard form.
-10
5.5 × 10
Standard Form
Calculations with Standard Form
•Work out the powers of 10 separately,
•Work out the number calculation
•Ensure the answer is in standard form
Example 1:
Calculate
4 × 104 × 2 × 103
104 ×103 = 107
4 ×2 = 8
Answer:
8 × 107
Standard Form
Example 2:
Calculate
8 × 105 × 7 × 104
105 ×104 = 109
8 ×7 = 56
56 × 109
This is not in standard form
Answer:
5.6 × 1010
Standard Form
Example 3:
Calculate
9 × 105 ÷ 3 × 102
105 ÷102 = 103
9÷ 3 = 3
3 × 103
Or it can be seen this way:
9 × 105
3 × 102
9 × 105
3 × 102
Cancelling common factors and
applying the index law for division
9 × 105
3 × 102
= 3 × 103
Standard Form
Example 3:
Calculate
1.8 × 106 ÷ 6 × 104
=
18 × 105
1.8 × 106
6 × 103
6 × 103
=
3 × 102
Standard Form
Now do these:
Calculate these and leave your answer in standard form:
1.
5000 × 3000
2.
1.5 × 107
3.
0.000 07 × 400
2.8 ×
5.
10-2
8 000 ÷ 0.004
3.0 × 108
4.
6.
5.4 × 107 ÷ 2 × 103
1.8 × 104 ÷ 9 × 10-2
2 × 105
-
0.000 033 ÷ 500
6.6 × 10-8
8.
2.7 × 104
9.
0.0007 × 0.000 01
7.0 × 10 8
2
7.
60 000 × 5 000
4.8 × 102 ÷ 3 × 104
1.6 × 10-2
10.
5.4 × 10-3 ÷ 2.7× 102
2 × 105