Standard Form in Scientific Notation:
Scientific notation is used to represent very large or very small numbers in a simplified and manageable way. It consists of two main components:
1. Coefficient (mantissa): This represents the significant digits of the number. It is a number greater than or equal to 1 and less than 10.
2. Base (exponent): This represents the power of 10 by which the coefficient is multiplied to obtain the original number. The exponent can be positive or negative.
Standard form in scientific notation is written as follows:
```
coefficient × 10^exponent
```
Examples of Standard Form (Scientific Notation):
1. The number 602,214,129,000,000,000,000,000 can be written in standard form as:
```
6.02214129 × 10^23
```
Here, the coefficient is 6.02214129, and the exponent is 23.
2. The number 0.00000000012 can be written in standard form as:
```
1.2 × 10^(-10)
```
Here, the coefficient is 1.2, and the exponent is -10.
Standard Form in Decimal Notation:
Standard form in decimal notation involves expressing numbers using place values and decimal points to separate whole numbers from decimal fractions. It ensures that the value of a number is clearly represented without scientific notation.
Standard form in decimal notation is written as follows:
```
[integral part]. [decimal part]
```
For example:
1. The number three thousand four hundred fifty-six point seven eight can be written in standard form as:
```
3456.78
```
2. The number zero point zero zero zero five can be written in standard form as:
```
0.00005
```
In summary, standard form in math refers to the consistent representation of numerical values using scientific notation or decimal notation, ensuring clarity and ease of understanding in mathematical calculations and expressions.