Generally,most students can write numbers in standard form while some cant,but here i will make every thing possible and to your understanding.
The introductory parts of this lesson is writing some numbers in standard for we say...
1000 = 10³ ---- we have 3 0s
100 = 10² ---- we have 2 0s
10 = 10¹ ---- only 1 (0)
1 = 10º none.
This is to say that, numbers are written in base 10.We can also express these in negative form.
1 1
0.01 = --------- = -------- = 10⁻²
100 10²
1 1
0.001= ------- = -------- 10⁻³
1000 10³
And so on.Therefore, the above method contains for higher and lower powers of ten (10).
Example 1
Let at something like these
(a)456
456 = 4.56 x 100
= 4.56 x 10²
In one hundred we have two zeros.
(b) 7329
7329 = 7.329 x 1000
= 7.329 x 10³
In one thousand, we have three zero
(c) 0.0034
0.0034 = 3.4 x 0.001
= 3.4 x 10⁻³
We have three negative zeros and 34,we mus always perpetrate them after one number.
Example 2
Write these in their standard form
(a) 4537000
(b) 0.00453
(c) 1.35 x 10⁻³
(d) 5.81 x 10³
Solution
(a) 4537000
4537000 = 4.537 x 1000 000
= 4.537 x 10⁶
When ever you are asked to solve any positive question like this, you count the number from your wright to your left as place value then you represent them as the power of 10. I mean, if you count this 4537000, you will see that we have six zeros after separating the first number with a decimal point,so we make it by writing 10 raise to power 6 it is a positive question and answer in standard form.
(b) 0.00453
0.00453 = 4.53 x 0.001
= 4.53 x 10⁻3
That is a negative expression.
(c) 1.35 x 10⁻³
1.35 x 10⁻³ = 1.35 x 0.001
= 0.00135
10⁻³ means, you keep the 3 (zeros) as 0.001, then the three zeros before the numbers by removing the point.This is also negative form
(d) 5.81 x 10³
5.81 x 10³ = 5.81 x 1000
multiply 5.81 by 1000
= 5810
Addition and Subtraction of Numbers in Standard Form
(Addition)
Example 3
Finding the sum of two standard form numbers can be done in two ways either by adding then of using factorisation method.
Find the sum of 7.95 x 10³ + 3.06 x 10³
= ( 7.95 x 1000) + (3.06 x 1000)
= 7950 + 3060
=1.101 x 10000 ( after the first 1, we have 4 digits numbers then you convert the digits to zeros. Always start with 1, before the zeros.)
= 1.101 x 10⁴
By using factorisation method we say:
=10³ ( 7.95 + 3.06)
=10³ (11.01)
=10³ x 1.101 x 10¹
=10 ⁽³⁺¹⁾ x 1.101
= 10⁴ x 1.101
=1.101 10⁴ x
(b) Find the sum of 7.95 x 10⁵ + 3.06 x 10⁶
= (9.17 x 100000 ) + (7.45x 1000000)
= 917000 + 7450000
= 8367000
= 8.367 x 10⁶
By using factorisation method we say:
= 10⁵ ( 9.17 + 7.45 x 10) the ten is in power 1.
= 10⁵ ( 917 + 74.5)
=10⁵ x 8.367 x 10
=10⁽⁵⁺¹⁾ x 8.367
= 10⁶ x 8.367
= 8.367 x 10⁶
Subtraction
(a)Find the value of 9.37 x 10⁴ - 3.5 x 10⁴.
9.37 x 10⁴ - 3.5 x 10⁴.
=( 9.37 x 10000) - ( 3.5 x 10000)
= 93700 - 35000
= 58700
= 5. 87 x 10⁴
(b) Find the value of 1.1 x 10⁻³ - 8.7 x 10⁻⁴
1.1 x 10⁻³ - 8.7 x 10⁻⁴
= (1.1 x 0.001 - ( 8.7 x 0.0001)
=0.0011 - 0.00087
=0.00023 ( here we have 4 zeros)
= 2. 3 x 10⁻⁴ (in standard form)
By using factorisation method we say:
1.1 x 10⁻³ - 8.7 x 10⁻⁴
= 10⁻³ (1.1 - 8.7 x 10⁻¹)
= 10⁻³ (1.1 - 0.87)
= 10⁻³ x 8.7 x 10⁻¹
=8.7 x 10⁻³⁻¹
= 8.7 x 10⁻⁴
Class Activities
Find the value of the following:
(a) 3.54 x 10⁴ + 12.4 x 10³
(b) 8.11 x 10⁻³ + 41.4 x 10⁻³
(c)54.3 x 10 ⁻³ - 9.4 x 10⁻⁶
(d) 12.34 x 10 ⁻⁶ - 3.7 x 10⁻¹
The above examples show you how to deal with standard form .Please if you have questions you are free to ask me by putting them in the comments box.
0 Comments