Final answer:
The decimal system utilizes digits 0-9 where each digit's value is based on its position relative to the decimal point. Scientific notation is a way of expressing very large or small numbers concisely, involving a coefficient and a power of 10. Zeros act as placeholders when moving the decimal point as needed.
Step-by-step explanation:
Understanding the Decimal System
The decimal system is a method of writing numbers that uses the base-10 system. This system utilizes the digits 0 through 9 to represent numbers. The value of each digit depends on its position relative to the decimal point. For instance, the number 231.45 can be broken down into its place values: 2 is in the hundreds place (200), 3 is in the tens place (30), 1 is in the ones place (1), 4 is in the tenths place (4/10 or 0.4), and 5 is in the hundredths place (5/100 or 0.05).
When dealing with numbers in scientific notation, we express very large or small numbers in a compact form. This involves writing a single nonzero digit, followed by a decimal point, and then the rest of the significant digits, which is multiplied by a power of 10 to represent the original number's scale. For example, 0.0000045 becomes 4.5 × 10-6. Zeros are used as place holders if there are not enough digits when moving the decimal point.
In scientific notation, the power of 10 reflects how many places the decimal point has been shifted. This is particularly useful for numbers of large or small magnitude, making calculations easier. For instance, 1,230,000,000 is written as 1.23 × 109, and 0.00000000036 is noted as 3.6 × 10-10.