Decimal Notation

Definition

Decimal notation is a way of representing numbers using a decimal point to indicate the place value of digits. It is a base-10 numeral system that uses the digits 0-9 and the decimal point to express both whole numbers and fractional parts.

5 Must Know Facts For Your Next Test

1. Decimal notation uses the decimal point to separate the whole number part from the fractional part of a number.
2. The digits to the left of the decimal point represent the whole number, while the digits to the right represent the fractional part.
3. Each digit in a decimal number has a place value that is a power of 10, with the rightmost digit representing the ones place, the next digit the tenths place, the next the hundredths place, and so on.
4. Decimal notation allows for the precise representation of quantities and measurements, making it essential for scientific and mathematical calculations.
5. Decimal numbers can be converted to and from other number systems, such as fractions and percentages, through the use of place value and conversion factors.

Review Questions

• Explain how decimal notation is used to represent both whole numbers and fractional parts.
  • Decimal notation uses the decimal point to separate the whole number part from the fractional part of a number. The digits to the left of the decimal point represent the whole number, while the digits to the right represent the fractional part. Each digit in the decimal part has a place value that is a power of 10, with the rightmost digit representing the ones place, the next digit the tenths place, the next the hundredths place, and so on. This allows for the precise representation of quantities and measurements, making decimal notation essential for scientific and mathematical calculations.
• Describe the relationship between decimal notation and exponential notation, particularly in the context of scientific notation.
  • Decimal notation and exponential notation are closely related, as decimal numbers can be expressed in exponential form. Scientific notation is a specific form of exponential notation used to represent very large or very small numbers as the product of a decimal between 1 and 10 and a power of 10. This allows for the compact and precise representation of numbers in scientific and mathematical contexts. The conversion between decimal notation and scientific notation involves identifying the appropriate power of 10 to scale the decimal part, demonstrating the interconnectedness of these two number representations.
• Analyze how the use of decimal notation enables the conversion between different number systems, such as fractions and percentages.
  • Decimal notation provides a bridge between different number systems, facilitating the conversion between quantities expressed as fractions, decimals, and percentages. The decimal point and place value structure of decimal notation allow for the precise representation of fractional parts, which can then be converted to equivalent forms, such as percentages, through the use of conversion factors. This flexibility and interoperability of decimal notation make it a fundamental tool in mathematics and science, enabling seamless transitions between various numerical representations and supporting complex calculations and analyses.

Related terms

Place Value: The value assigned to a digit based on its position in a number, with each place representing a power of 10.

Exponential Notation: A way of writing very large or very small numbers using exponents to indicate the power of 10.

Scientific Notation: A form of exponential notation used to represent numbers as the product of a decimal between 1 and 10 and a power of 10.