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Decimal numbers and fractions are two different ways of expressing a non-whole value or ratio. Both have unique features and applications, and understanding the relationship between decimals and fractions can assist in many mathematical calculations and concepts.
A decimal number is a number that contains a whole number and a part of a whole number, separated by a decimal point. This part of the whole number is called a decimal part. The decimal system is based on 10, which means that each digit in the decimal number represents a power of 10. For example, in the number 123.456, 123 represents the whole parts, and 456 represents parts of a whole, namely 4 tenths, 5 hundredths, and 6 thousandths.
A fraction, on the other hand, consists of two numbers, separated by a fraction line. The number above the line is the numerator, which indicates how many parts of the whole are taken. The number below the line is the denominator, which indicates into how many parts the whole is subdivided. So, in the fraction 3/4, the numerator is 3 and the denominator is 4, meaning that we are taking 3 parts of a whole that is subdivided into 4 parts.
Converting decimals to fractions and vice versa is a common mathematical operation. For example, when we convert a decimal to a fraction, we take the part behind the decimal point as the numerator and the value of the place of the last digit of the decimal value as the denominator. Then we reduce the fraction to the simplest form. For example, the decimal 0.75 can be converted to the fraction 75/100, which can be reduced to 3/4.
Conversely, to convert a fraction to a decimal, we simply divide the numerator by the denominator. So, the fraction 3/4 becomes 0.75 in decimal form.
In many situations, it can be more convenient to work with decimals than with fractions, especially in calculations dealing with measurements, money, or data in scientific and technical contexts. However, fractions can be more useful in solving problems that describe parts of a whole or a ratio.
It's important to remember that although decimals and fractions can represent information in different ways, both are valuable tools in mathematics to help us understand and work with non-whole numbers.