"The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers."
The process of determining which of two or more decimals is greater or smaller, and arranging decimals in order from least to greatest or greatest to least.
Decimal Notation: Understanding what decimal numbers are and how to write them in decimal notation.
Place Value: Knowing the value of each digit in a decimal number based on its position.
Comparing Decimals: Learning the symbols (<, >, and =) used to compare decimal numbers and how to use them to compare decimal values.
Rounding Decimals: Understanding how to round decimal numbers to the nearest whole number, tenth, hundredth, or thousandth.
Adding and Subtracting Decimals: Knowing how to add and subtract decimal numbers, including carrying and borrowing with decimals.
Multiplying Decimals: Understanding how to multiply decimal numbers, including insights into place value and patterns.
Dividing Decimals: Knowing how to divide decimal numbers, including long division with decimals and understanding the importance of estimating.
Word Problems: Solving real-world problems that involve decimal numbers, such as measuring length, weight, or money.
Decimal Place Value Chart: Understanding the organization and structure of the decimal place value chart and how to use it to compare and order decimal numbers.
Fraction-Decimal Equivalents: Understanding the relationship between fractions and decimals, including converting fractions to decimals.
Ordering Decimals: Learning how to put decimal numbers in order from highest to lowest or lowest to highest, as well as understanding the importance of comparing like values.
Decimals with Different Numbers of Digits: Handling comparisons and calculations with decimals that have varying numbers of digits before and after the decimal point.
Decimal Estimation: Knowing how to estimate decimal numbers mentally or through rounding to simplify calculations or to check the reasonableness of an answer.
Practical Applications of Decimal Arithmetic: Understanding the importance of decimals in everyday life, including financial management, scientific calculations, and data analysis.
Comparing Decimal Numbers: In this type, you are required to compare two decimal numbers and determine which one is greater or smaller.
Ordering Decimal Numbers: In this type, you are required to arrange a set of decimal numbers in ascending or descending order, depending on the given instructions.
Decimal Place Value: Decimal place value is an essential aspect of comparing and ordering decimals. You must understand how the decimal point affects the value of the given decimal number.
Rounding Decimals: Rounding decimals is another important skill required to compare and order decimals accurately. In this type, you must round a decimal number to a specific decimal place based on the given instructions.
Repeating Decimals: Repeating decimals are decimal numbers that have a repeating pattern of digits after the decimal point. In this type, you must understand how repeating decimals work and how to compare and order them.
Scientific Notation: Scientific notation is a way of expressing very large or very small numbers using powers of 10. In this type, you must know how to convert a decimal number into scientific notation to compare and order them accurately.
Mixed Decimal Numbers: Mixed decimal numbers are decimal numbers that have a whole number and a fractional part. In this type, you must know how to compare and order mixed decimal numbers correctly.
Word Problems: In this type, you will encounter real-life scenarios where you must compare and order decimal numbers to solve a problem. You must know how to identify the relevant information and apply the appropriate arithmetic operations to arrive at a solution.
"It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system."
"The way of denoting numbers in the decimal system is often referred to as decimal notation."
"Decimals may sometimes be identified by a decimal separator (usually "." or "," as in 25.9703 or 3,1415)."
"Decimal may also refer specifically to the digits after the decimal separator, such as in '3.14 is the approximation of π to two decimals'."
"Zero-digits after a decimal separator serve the purpose of signifying the precision of a value."
"The numbers that may be represented in the decimal system are the decimal fractions."
"That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer."
"The decimal system has been extended to infinite decimals for representing any real number, by using an infinite sequence of digits after the decimal separator."
"In this context, the decimal numerals with a finite number of non-zero digits after the decimal separator are sometimes called terminating decimals."
"A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits."
"An infinite decimal represents a rational number, the quotient of two integers if and only if it is a repeating decimal or has a finite number of non-zero digits."
"The decimal numeral system (also called the base-ten positional numeral system and denary or decanary)."
"It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system."
"A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system."
"Decimals may sometimes be identified by a decimal separator (usually "." or "," as in 25.9703 or 3,1415)."
"Zero-digits after a decimal separator serve the purpose of signifying the precision of a value."
"The numbers that may be represented in the decimal system are the decimal fractions."
"That is, fractions of the form a/10n, where a is an integer, and n is a non-negative integer."
"A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits."