Decimal definition
A decimal is a number written using a decimal point to show parts of a whole. The digits to the left of the decimal point represent whole numbers, and the digits to the right represent fractions of one. For example, 3.5 means 3 whole units and 5 tenths. The decimal point separates the whole-number part from the fractional part of the number.
Decimal place value is very important. In the number 12.347, the 1 is in the tens column, the 2 is in the ones column, the 3 is in the tenths column, the 4 is in the hundredths column and the 7 is in the thousandths column. Each place becomes ten times smaller as you move to the right. This is why 0.3 is bigger than 0.03, even though 3 and 3 look similar as digits.
Decimals are used in many maths topics, including number, fractions, percentages, ratio, proportion, measures, money, probability, statistics, standard form and algebra. At GCSE level, students use decimals when ordering numbers, rounding answers, calculating with money, converting units, reading scales, solving percentage problems and interpreting data. At A-Level, decimals still appear in modelling, numerical methods, mechanics, statistics and calculator-based answers.
Decimals are closely connected to fractions. The decimal 0.5 is the same as 1/2 because five tenths is equivalent to one half. The decimal 0.25 is the same as 1/4, and 0.75 is the same as 3/4. Percentages are also connected to decimals: 0.6 is 60%, 0.08 is 8%, and 1.25 is 125%. A useful rule is percentage = decimal × 100.
Decimals can be terminating or recurring. A terminating decimal ends, such as 0.4, 2.75 or 0.125. A recurring decimal has a digit or group of digits that repeats forever, such as 0.333... for 1/3. Recurring decimals are often shown with dots or a bar over the repeating digits. Understanding this helps students see why some fractions convert neatly to decimals and others do not.
Rounding decimals is a common exam skill. If a question asks for 3.746 to two decimal places, you look at the third decimal digit. The number becomes 3.75 because the third decimal digit is 6, so the second decimal place rounds up. If the number was 3.742, it would round to 3.74. Rounding must be done carefully because premature rounding can make later answers inaccurate.
Decimals are also used in real life every day. Money uses decimals because £4.50 means four pounds and fifty pence. Measurements use decimals when recording lengths, masses, temperatures and times. Sports statistics, science results, fuel prices, exchange rates and exam scores can all be written as decimals. This makes decimal understanding useful beyond the classroom.
Related formulas and ideas include place value, decimal × 100 = percentage, percentage ÷ 100 = decimal, fraction to decimal conversion, rounding to decimal places, significant figures and standard form. A strong definition of decimal helps students understand that decimals are not separate from fractions and percentages. They are another way of writing parts of a whole, using the base-ten number system.