Decimals – iGCSE Mathematics OxfordAQA Revision

Decimals represent fractions where the denominator is a power of ten.
A decimal includes a decimal point and digits that represent tenths, hundredths, thousandths, and so on.
The digits to the left of the decimal point represent whole numbers while the digits to the right represent fractional parts of a whole.

Addition and Subtraction: To add or subtract decimals, line them up by their decimal points and add or subtract as you would whole numbers. Remember to place the decimal point in the correct place in the answer.
Multiplication: To multiply decimals, ignore the decimal points and multiply as if they are whole numbers. Then, count the total number of digits to the right of the decimal points in the original numbers and place the decimal point in the answer so there are that many digits to its right.
Division: To divide decimals, move the decimal point in the divisor (the number you are dividing by) to the right until it becomes a whole number. Then move the decimal point in the dividend (the number you are dividing) the same number of places to the right. Now divide as if they are whole numbers.

Converting decimals to fractions: Write the digits to the right of the decimal point as the numerator and the denominator as the number represented by a 1 followed by as many zeroes as there are digits to the right of the decimal point. Then simplify the fraction as much as possible.
Converting fractions to decimals: Divide the numerator by the denominator using long division. If the division does not terminate, indicate the repeating digits by placing a bar over them.

Terminating decimals: Decimals where the digits after the decimal point end.
Recurring decimals: Decimals where the digits after the decimal point continue in a regular repeat pattern.
Round off decimals: Reducing the number of digits after the decimal point to make calculations easier or to give an approximate answer. It’s important to follow the rules of rounding correctly.

Be cautious about the placement of the decimal point. Misplacing it can significantly change the magnitude of a number.
When performing decimal operations, always be mindful of aligning decimal points correctly for addition, subtraction and multiplying the numbers as if they were whole numbers.
Always remember to practise problems related to decimals. From basic operations to rounding off, converting between decimals and fractions, these skills are fundamental for numerical proficiency.