Let's tackle each part of the problem step-by-step and convert the given numbers and expressions into scientific notation.
### Part i: Convert 14560000000 into Scientific Notation
To convert the number 14560000000 into scientific notation, we need to express it in the form [tex]\( a \times 10^n \)[/tex] where [tex]\( 1 \leq a < 10 \)[/tex].
1. Move the decimal point to the left until only one non-zero digit remains to the left.
2. Count the number of places the decimal point has moved. This number becomes the exponent [tex]\( n \)[/tex].
For the number 14560000000:
- The decimal point moves 10 places to the left.
- Therefore, [tex]\( 14560000000 = 1.46 \times 10^{10} \)[/tex].
### Part ii: Convert 0.000045 into Scientific Notation
Similarly, to convert 0.000045 into scientific notation:
1. Move the decimal point to the right until only one non-zero digit remains to the left.
2. Count the number of places the decimal point has moved. This number becomes the negative exponent [tex]\( n \)[/tex].
For the number 0.000045:
- The decimal point moves 5 places to the right.
- Therefore, [tex]\( 0.000045 = 4.50 \times 10^{-5} \)[/tex].
### Part iv: Evaluate and Convert [tex]\( 7.35 \times 10^5 \times 4 \times 10 \)[/tex]
To solve this expression, follow these steps:
1. Combine the constants:
- [tex]\( 7.35 \times 4 \times 10 = 29.4 \times 10 \)[/tex]
2. Now, [tex]\( 29.4 \times 10^5 \times 10 \)[/tex] can be represented as:
- [tex]\( 29.4 \times 10^6 \)[/tex]
3. Finally, convert [tex]\( 29.4 \times 10^6 \)[/tex] to standard scientific notation:
- [tex]\( 29.4 \)[/tex] can be written as [tex]\( 2.94 \times 10 \)[/tex]
- Hence, [tex]\( 2.94 \times 10 \times 10^6 = 2.94 \times 10^7 \)[/tex]
### Part v: Evaluate and Convert [tex]\( 5.30 \times 10^{-2} \times 2 \times 10^2 \)[/tex]
To solve this expression, follow these steps:
1. Combine the constants:
- [tex]\( 5.30 \times 2 = 10.60 \)[/tex]
2. Now, [tex]\( 10.60 \times 10^{-2} \times 10^2 \)[/tex] can be represented as:
- [tex]\( 10.60 \times 10^{0} = 10.60 \)[/tex]
3. Finally, convert [tex]\( 10.60 \)[/tex] to standard scientific notation:
- [tex]\( 10.60 \)[/tex] can be written as [tex]\( 1.06 \times 10^1 \)[/tex]
### Answers Summary:
i. [tex]\( 14560000000 \)[/tex] in scientific notation is [tex]\( 1.46 \times 10^{10} \)[/tex].
ii. [tex]\( 0.000045 \)[/tex] in scientific notation is [tex]\( 4.50 \times 10^{-5} \)[/tex].
iv. [tex]\( 7.35 \times 10^5 \times 4 \times 10 \)[/tex] in scientific notation is [tex]\( 2.94 \times 10^{7} \)[/tex].
v. [tex]\( 5.30 \times 10^{-2} \times 2 \times 10^2 \)[/tex] in scientific notation is [tex]\( 1.06 \times 10^{1} \)[/tex].
