The numbers written to the power of 10 in the representation of decima...
Explanation:
The correct answer is option C, scale factors.
Decimal Numbers:
Decimal numbers are numbers that are expressed in the base-10 numbering system. In this system, each digit's value is determined by its position relative to the decimal point.
Powers of 10:
In the representation of decimal numbers, each digit's value is multiplied by a power of 10 based on its position. These powers of 10 are called scale factors.
Significance of Scale Factors:
Scale factors play a crucial role in determining the magnitude or size of a decimal number. They help establish the relationship between the digit's position and its value.
Example:
Let's consider the decimal number 123.45. In this number, the digit '1' represents hundreds, '2' represents tens, '3' represents units, '4' represents tenths, and '5' represents hundredths.
The scale factors for these digits are as follows:
- '1' is multiplied by 10^2 (10 raised to the power of 2) to represent hundreds.
- '2' is multiplied by 10^1 (10 raised to the power of 1) to represent tens.
- '3' is multiplied by 10^0 (10 raised to the power of 0) to represent units.
- '4' is multiplied by 10^(-1) (10 raised to the power of -1) to represent tenths.
- '5' is multiplied by 10^(-2) (10 raised to the power of -2) to represent hundredths.
These scale factors ensure that the digits are correctly positioned and contribute to the overall value of the decimal number.
Conclusion:
In the representation of decimal numbers, the numbers written to the power of 10 are called scale factors. Scale factors help determine the magnitude or size of a decimal number by establishing the relationship between the digit's position and its value.