Convert the following into scientific notation:

i. [tex]\(14560000000\)[/tex]

ii. [tex]\(0.000045\)[/tex]

iii. [tex]\(7.35 \times 10^5 \times 4 \times 10\)[/tex]

iv. [tex]\(5.30 \times 10^{-2} \times 2 \times 10^2\)[/tex]

Convert the following scientific notations into standard form:



Answer :

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].