Decimal Fraction: Definition, Examples, and Applications

Decimal fraction is a type of number that is used to represent numbers in a fractional form. It is also known as a decimal or a decimal number. The decimal fraction is a system of numbers that is based on the decimal point. The decimal point is used to separate the whole number from its fractional part. In this system, the whole numbers are represented to the left of the decimal point, and the fractional numbers are represented to the right of the decimal point.

Decimal fractions are very important in everyday life, and they are used in many different applications. For example, they are used in financial calculations, measurements, and scientific calculations. Decimal fractions are used in many different fields such as physics, engineering, and mathematics.

The decimal system is based on the number 10, and this means that each digit in a decimal number represents a power of 10. The digit to the right of the decimal point represents the tenths place, the digit two places to the right of the decimal point represents the hundredths place, and so on.

For example, the number 123.45 can be represented as follows:

1 x 10^2 + 2 x 10^1 + 3 x 10^0 + 4 x 10^-1 + 5 x 10^-2

In this example, the digit 1 represents the hundreds place, the digit 2 represents the tens place, and the digit 3 represents the ones place. The digit 4 represents the tenths place, and the digit 5 represents the hundredths place.

Decimal fractions can be added, subtracted, multiplied, and divided just like whole numbers. To add or subtract decimal fractions, the numbers must be lined up by their decimal points. To multiply decimal fractions, the numbers are multiplied together, and then the decimal point is placed in the product based on the number of decimal places in the factors. To divide decimal fractions, the divisor is multiplied by a power of 10 to make it a whole number, and then the dividend is divided by the divisor.

For example, to add the numbers 1.23, 4.56, and 7.89, the numbers must be lined up by their decimal points as follows:

• 4.56
• 7.89 ====== 13.68

To multiply the numbers 1.23 and 4.56, the numbers are multiplied together as follows:

1.23 x 4.56

6156

The decimal point is placed in the product based on the number of decimal places in the factors, which is two decimal places. Therefore, the product is 6.156.

Decimal fractions can also be converted to fractions with denominators of 10, 100, 1000, and so on. To convert a decimal fraction to a fraction, the decimal is written as the numerator, and the denominator is written as 1 followed by the same number of zeros as there are decimal places.

For example, the decimal fraction 0.25 can be written as the fraction 25/100 or 1/4. The decimal fraction 0.125 can be written as the fraction 125/1000 or 1/8.

Definition of Decimal Fraction

A decimal fraction is a fraction whose denominator is a power of ten, expressed as a decimal point followed by one or more digits. The denominator of a decimal fraction is always 10, 100, 1000, or a power of 10. For example, 0.5 is a decimal fraction because its denominator is 10. Similarly, 0.25 is a decimal fraction because its denominator is 100, and 0.125 is a decimal fraction because its denominator is 1000.

Decimal fractions can be represented as a decimal point followed by one or more digits. For example, 0.25 can be written as 0.25, and 0.125 can be written as 0.125. Decimal fractions can also be expressed in scientific notation, where a number is expressed as a product of a decimal fraction and a power of 10. For example, 0.25 can be expressed in scientific notation as 2.5 × 10^-1.

Properties of Decimal Fractions

Decimal fractions have several properties that are important to understand. These properties include:

• Place Value: Each digit in a decimal fraction has a specific place value. The first digit to the right of the decimal point represents tenths, the second digit represents hundredths, and so on. For example, in the decimal fraction 0.25, the 2 represents two tenths, and the 5 represents five hundredths.
• Rounding: Decimal fractions can be rounded to a specified number of decimal places. To round a decimal fraction, identify the digit in the specified decimal place and determine whether to round up or down based on the digit to the right of it. For example, to round 0.456 to two decimal places, we would look at the digit in the hundredths place (5) and round up to 0.46.
• Addition and Subtraction: Decimal fractions can be added and subtracted in the same way as whole numbers. To add or subtract decimal fractions, align the decimal points and perform the operation as usual. For example, to add 0.25 and 0.75, we would align the decimal points and get 1.00.
• Multiplication: Decimal fractions can be multiplied by whole numbers or other decimal fractions. To multiply decimal fractions, ignore the decimal points and perform the multiplication as usual. Then, count the total number of digits to the right of the decimal point in both factors and place the decimal point in the product that many places from the right. For example, to multiply 0.25 and 0.5, we would ignore the decimal points and get 125. Then, since there are two digits to the right of the decimal point in the factors, we would place the decimal point two places from the right in the product to get 0.125.
• Division: Decimal fractions can be divided by whole numbers or other decimal fractions. To divide decimal fractions, move the decimal point in the divisor to the right until it becomes a whole number. Then, move the decimal point in the dividend the same number of places to the right. Finally, perform the division as usual.

In conclusion, decimal fractions are an important part of everyday life, and they are used in many different applications. They are used in financial calculations, measurements, and scientific calculations. The decimal system is based on the number 10, and this means that each digit in a decimal number represents a power of 10. Decimal fractions can be added, subtracted, multiplied, and divided just like whole numbers.

Quiz

1. What is a decimal fraction? Answer: A decimal fraction is a fraction expressed with a decimal point, where the denominator is a power of ten.
2. How is a decimal fraction different from a regular fraction? Answer: A regular fraction is expressed as a ratio of two integers, while a decimal fraction is expressed with a decimal point and a denominator that is a power of ten.
3. What is the decimal equivalent of 3/5? Answer: The decimal equivalent of 3/5 is 0.6.
4. How do you convert a fraction to a decimal? Answer: To convert a fraction to a decimal, divide the numerator by the denominator.
5. What is the decimal equivalent of 1/4? Answer: The decimal equivalent of 1/4 is 0.25.
6. What is the decimal equivalent of 7/8? Answer: The decimal equivalent of 7/8 is 0.875.
7. What is the decimal equivalent of 5/6? Answer: The decimal equivalent of 5/6 is 0.8333 (repeating).
8. How do you round a decimal to the nearest hundredth? Answer: To round a decimal to the nearest hundredth, look at the third digit after the decimal point. If it is 5 or greater, round up; if it is less than 5, round down.
9. What is the decimal equivalent of 2/3? Answer: The decimal equivalent of 2/3 is 0.6666 (repeating).
10. What is the decimal equivalent of 3/8? Answer: The decimal equivalent of 3/8 is 0.375.

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