Answer:
The answer to your question is:
Explanation:
e) 9.10 x 10³ + 2.2 x 10⁶ = 2.2091 x 10⁶
f) 1113.0 - 14.6 x 10² = -347 = -3.47 x 10²
g) 6.18 x 10⁻⁴⁵ + 4.72 x 10⁻⁴⁴ = 5.338 x 10⁻⁴⁴
h) 4.25 x 10⁻³ - 1.6 x 10⁻² = -0.01175 = -1.175 x 10 ⁻²
5.- Calculate ...
a) 2.63 x 10⁻⁴
b) 2.26 x 10¹³
c) 1.97 x 10²
d) 1.65 x 10⁻²³
e) 2.5 x 10⁻⁸³
f) 1.61 x 10¹⁴
g) 2 x 10⁷⁹
h) 2.37 x 10⁻⁷
Explanation:
Scientific notation is written in the form
[tex]a \times {10}^{n} [/tex]
n is an integer between 1 and 10
Positive integer as exponent means a large number
Negative integer as exponent means small number
e.
First we have to add 9.10 and 2.20
[tex]9.10 + 2.20 = 12.30[/tex]
But the number has to be between 1 and 10 so we move the decimal one place to the right
[tex] = 1.23[/tex]
Then we have to add the exponent
[tex] {10}^{3} + {10}^{6} [/tex]
We are only adding the exponent
[tex]3 + 6 = 9[/tex]
Because we moved the decimal one place more we add
[tex]9 + 1 = 10[/tex]
So the answer is
[tex]1.23 \times {10}^{10} [/tex]
f.
The problem is
[tex]1113.0 - 14.6 \times {10}^{2} [/tex]
There is a problem. The problem is one is at scientific notation a d the other isn't. So we have to turn 1113.0 to a scientific notion by moving the decimal three places to the left
[tex]1.113 \times {10}^{3} [/tex]
We also have another problem. The problem is 14.6 as we said before it has to be between 1 and 10 so we just have to move the decimal to the left on time
[tex]1.46 \times {10}^{3} [/tex]
The we just add 2+1 to get 3
Now we just subtract
[tex]1.113 - 1.46[/tex]
[tex] = - .347[/tex]
Because it has to be between 1 and 10 we move one place to the right
[tex] - 3.47[/tex]
When we subtract 3 and 3 we get zero but because we moved one place to the right we get
[tex] {10}^{ - 1} [/tex]
So the answer is
[tex]3.47 \times {10}^{ - 1} [/tex]
a.
The problem is
[tex] \frac{3.95 \times {10}^{2} }{1.15 \times {10}^{6} } [/tex]
The first step is to divide
[tex] \frac{3.95}{1.15} = 3.434782609[/tex]
The we subtract the exponent
[tex]2 - 6 = - 4[/tex]
So the answer is
[tex]3.434782609 \times {10}^{ - 4} [/tex]
b.
This problem is
[tex](3.5 \times {10}^{2} ) \times (6.45 \times {10}^{10} )[/tex]
First we multiply
[tex]3.5 \times 6.45 = 22.575[/tex]
Because it has to be between 1 and 10 we have to move the decimal to the right
[tex]2.2575[/tex]
Now we add the exponent
[tex]10 + 2 = 12[/tex]
But we also have to add one because we moved the decimal to so we add 1 to it so we get 13
The answer is
[tex]2.2575 \times {10}^{13} [/tex]
