Introduction
Decimal fractions are a special way of representing parts of a whole where the denominator is a power of 10, such as 10, 100, or 1000. Instead of using a fraction bar, we use a decimal point to separate the whole number from the fractional part.
Explanation Step by Step
To understand decimal fractions, we must look at the place value system. When we move to the right of the units place, we use a dot called the decimal point.
| Tens | Units | Decimal Point | Tenths (1/10) | Hundredths (1/100) |
|---|---|---|---|---|
| 1 | 5 | . | 7 | 5 |
Sub-topics
Reading and Writing Decimal Fractions
A fraction like 5/10 is written as 0.5 and read as "zero point five". If we have a mixed fraction like 3 and 4/10, it is written as 3.4.
Examples
Example 1: Writing 7/10
Addition and Subtraction
When adding or subtracting decimal fractions, always line up the decimal points vertically.
Examples
Example 1: 12.50 + 4.25
Tricks and Shortcuts
To quickly convert a fraction with a denominator of 100 to a decimal, count two places from the right and place the decimal point. For example, 45/100 becomes 0.45.
Common Mistakes
Students often forget to align the decimal points during subtraction, leading to incorrect calculations. Always add placeholder zeros if the number of digits after the decimal differs.
Practice Questions
Easy Questions
- Write 9/10 in decimal form.
- Read the decimal fraction 0.4.
- Identify the digit in the tenths place in 15.6.
Medium Questions
- Add 4.5 and 3.2.
- Write 25/100 as a decimal fraction.
- Subtract 2.1 from 5.8.
Hard Questions
- Find the sum of 12.75 and 8.3.
- Subtract 4.56 from 10.
- What is the place value of 5 in 12.35?
Revision Summary
Decimal fractions use a decimal point. The first place to the right is tenths, and the second is hundredths. Always align the point for addition and subtraction.