Decimals are a way to represent fractions in a decimalized form. In decimal notation, the fraction is represented as a number with a decimal point, with the numerator of the fraction being the digits to the right of the decimal point and the denominator being a power of 10.
For example, the fraction 3/10 can be represented as the decimal 0.3, while the fraction 7/25 can be represented as the decimal 0.28.
Decimals can also be used to represent whole numbers with a fractional part. For example, the number 5.25 can be read as "five and twenty-five hundredths."
When performing arithmetic operations with decimals, it is important to pay attention to the place value of each digit. The place value of a digit in a decimal is determined by its position to the right of the decimal point. For example, in the number 12.345, the digit 4 has a place value of 0.004 because it is four places to the right of the decimal point.
It is also important to understand how to compare decimals. When comparing two decimals, start by comparing the digits to the left of the decimal point. If the digits are the same, move to the right until you find a different digit. The decimal with the larger digit in that position is the larger of the two decimals.
In addition to arithmetic operations and comparisons, decimals are used in a variety of contexts, including measurements, money, and scientific notation.
Operating with decimals involves performing arithmetic operations (addition, subtraction, multiplication, and division) using decimal numbers.
Addition and Subtraction:
To add or subtract decimal numbers, align the decimal points of the numbers and perform the operation as you would with whole numbers. When adding or subtracting, it is important to carry any extra digits to the left of the decimal point.
For example:
3.2 + 2.75 = 5.95
7.6 - 4.28 = 3.32
Multiplication:
To multiply decimal numbers, first multiply the numbers as if they were whole numbers. Then, count the total number of digits to the right of the decimal points in the numbers being multiplied. Place the decimal point in the answer so that there are that many digits to the right of the decimal point.
For example:
1.5 x 2.4 = 3.6
4.7 x 0.3 = 1.41
Division:
To divide decimal numbers, first move the decimal point in the divisor (the number being divided into the other number) to the right until it becomes a whole number. Then, move the decimal point in the dividend (the number being divided) the same number of places to the right. Perform the division as you would with whole numbers.
For example:
15.6 ÷ 3 = 5.2
2.52 ÷ 0.6 = 4.2
It is important to be precise when working with decimals, paying close attention to the placement of the decimal point and carrying any extra digits when necessary. It is also helpful to use estimation to check the reasonableness of your answer.