Fractions and recurring decimals

Fractions

A fraction represents a part of a whole. It is composed of a numerator (the top number) and a denominator (the bottom number). The numerator signifies how many parts we have, while the denominator tells us the total number of equal parts.
For instance, in the fraction 3/4, 3 is the numerator and 4 is the denominator. It indicates that we have 3 out of 4 equal parts.
A proper fraction is one where the numerator is less than the denominator, such as 3/4. An improper fraction has a numerator equal to or greater than the denominator, for example, 5/4 or 4/4.
A mixed number is composed of a whole number and a fraction, for example, 1 3/4.

Recurring Decimals

A recurring decimal is a decimal number that has digits which repeat forever. The recurring part is often marked with a dot above the first and last digit of the repeating sequence. For instance, 0.666… can be written as 0.6̅.
All fractions can be converted into decimal numbers. Some fractions convert into finite decimals, while others convert into recurring decimals.
For example, 3/4 = 0.75 (a finite decimal) whereas 1/3 = 0.3̅ (a recurring decimal).

Converting Fractions to Decimals

To convert a fraction into a decimal, divide the numerator by the denominator.
For example, to convert 3/4 into a decimal, divide 3 by 4, which gives us 0.75.
If the decimal repeats, it may be easier to identify the repeating pattern and write it as a recurring decimal.

Converting Recurring Decimals to Fractions

Converting recurring decimals to fractions can be a bit more challenging and may require some algebraic manipulation.
For example, to convert the recurring decimal 0.6̅ to a fraction, let x = 0.6̅. Multiply both sides by 10 to shift the decimal point, giving 10x = 6.6̅. Subtract the original equation from this to get 9x = 6, and then solve for x to find that x (0.6̅) is equal to 6/9, which simplifies to 2/3.

Real-life Applications

Understanding fractions and recurring decimals can help solve problems in various real-life situations, such as calculating discounts, dividing portions, understanding statistical data, and working with measurements or percentages.