Learning Objectives
- Understand the concept of decimals and their place values
- Convert fractions to decimals and decimals to fractions
- Compare and order decimal numbers
- Perform addition and subtraction of decimals
- Use decimals in everyday life — money, length, weight
Key Concepts
What Are Decimals?
Decimals are another way of representing fractions whose denominators are 10, 100, 1000, etc. The dot (.) is called the decimal point. The digits to the left of the decimal point form the whole number part, and the digits to the right form the decimal part. For example, in 25.73, the whole part is 25 and the decimal part is 73.
Place Value in Decimals
Each position after the decimal point represents a fraction. The first place after the decimal is tenths (1/10), the second is hundredths (1/100), and the third is thousandths (1/1000). For example, 3.45 = 3 + 4/10 + 5/100 = 3 + 0.4 + 0.05.
Conversion Between Fractions and Decimals
To convert a fraction to a decimal, divide the numerator by the denominator. For example, 3/4 = 0.75. To convert a fraction with denominator 10 or 100, simply place the decimal point. Example: 7/10 = 0.7 and 23/100 = 0.23.
To convert a decimal to a fraction, write the decimal as a fraction with the appropriate power of 10 as the denominator. Example: 0.6 = 6/10 = 3/5.
Comparing Decimals
First compare the whole number parts. If they are the same, compare the tenths place, then the hundredths place, and so on. For example, 4.56 > 4.52 because at the hundredths place, 6 > 2. Adding zeros after the last decimal digit does not change the value: 3.5 = 3.50 = 3.500.
Addition and Subtraction of Decimals
Align the decimal points vertically and add or subtract as you would with whole numbers. Fill in empty decimal places with zeros. Example: 12.6 + 3.45 → write as 12.60 + 3.45 = 16.05.
Decimals in Daily Life
Money: Rs 15.50 means 15 rupees and 50 paise. Length: 2.5 m means 2 metres and 50 centimetres. Weight: 1.25 kg means 1 kilogram and 250 grams.
Summary
Decimals extend the place value system to represent parts of a whole. They are closely related to fractions with denominators of 10, 100, etc. We can convert between fractions and decimals easily. Comparing, adding, and subtracting decimals requires aligning the decimal points properly.
Important Terms
- Decimal Point: The dot that separates the whole number part from the fractional part
- Tenths: The first place to the right of the decimal point (1/10)
- Hundredths: The second place to the right of the decimal point (1/100)
- Thousandths: The third place to the right of the decimal point (1/1000)
- Like Decimals: Decimals with the same number of decimal places
Quick Revision
- 0.1 = 1/10, 0.01 = 1/100, 0.001 = 1/1000
- Adding zeros to the right of the last decimal digit does not change the value
- 1 rupee = 100 paise, so 1 paisa = Rs 0.01
- 1 km = 1000 m, so 1 m = 0.001 km
- 1 kg = 1000 g, so 1 g = 0.001 kg
- Always align decimal points when adding or subtracting
- A decimal can be read as: 4.35 → four point three five