Decimals: Explained with Examples, A Complete Student Guide

A decimal is a way of writing a number that has a whole part and a fractional part, joined by a decimal point. In the number 4.75, the 4 is the whole part and 75 stands for 75 hundredths. Decimals are simply another way of writing fractions whose denominators are 10, 100, 1000 and so on: 0.75 is exactly the same as 75/100.

Decimals matter because the real world runs on them. Money is counted in rupees and paise (Rs. 24.50), medicines are measured in millilitres (2.5 mL), and exam marks are often recorded as 87.5. If you can read, compare and calculate with decimals, daily tasks like shopping and measuring become easy.

Key Concepts

• Decimal point: the dot that separates the whole part of a number from its fractional part. Everything to the left is whole; everything to the right is a fraction of one.
• Place value: the first digit after the point is tenths (1/10), the second is hundredths (1/100), the third is thousandths (1/1000). In 4.758, the 7 means 7 tenths.
• Terminating decimal: a decimal that ends, such as 0.75 or 3.125.
• Non-terminating decimal: a decimal that goes on forever, such as 0.333… (which equals 1/3).
• Like decimals: decimals with the same number of digits after the point, like 0.50 and 0.25, which makes comparison easy.

How It Works

1. Addition and subtraction: line up the decimal points, pad with zeros so both have the same digits after the point, then add or subtract as usual.
2. Multiplication: ignore the decimal points and multiply the whole numbers. Count the total number of digits after the point in both numbers, then place the point in the answer so it has exactly that many digits after it.
3. Division: move the decimal point of the divisor to the right until it becomes a whole number, then move the point of the dividend the same number of places. Divide as usual.

Worked Example

Multiply 3.75 by 2.4.

1. Ignore the points and multiply 375 by 24. First 375 x 20 = 7500, then 375 x 4 = 1500, and 7500 + 1500 = 9000.
2. Count decimal digits: 3.75 has 2 and 2.4 has 1, so the answer needs 3 digits after the point.
3. Place the point in 9000 to get 9.000, which is simply 9. So 3.75 x 2.4 = 9.

Common Misconceptions

• “0.45 is bigger than 0.5 because 45 is bigger than 5.” Wrong. Write 0.5 as 0.50, and 0.50 is clearly larger than 0.45. Always compare digit by digit starting from the decimal point.
• “A decimal is always smaller than 1.” Wrong. Only the fractional part is smaller than 1; 7.25 is bigger than 1 and bigger than 7.
• “More digits after the point means a bigger number.” Wrong. 0.456 is smaller than 0.5, because in the tenths place 4 is less than 5.

Real-World Applications

• Shops and banks use decimals for money: Rs. 24.50, interest rates like 7.25 percent, and bills.
• Scientists and doctors use decimals for precise measurement: 2.5 mL medicine doses, 9.58 seconds in a 100 m sprint.
• Engineers use decimals for lengths, such as a 12.5 mm bolt or a pipe of diameter 2.75 cm.

Decimals are fractions written with a point. Line up the points when adding, count the decimal digits when multiplying, and compare digit by digit from the left — then decimals feel as natural as whole numbers.