Class 6 Maths Decimals Notes

Introduction:
The chapter “Decimals” helps students understand numbers that are less than one and how to represent and operate on them. Decimals are used in various real-life scenarios, such as measuring distances, weights, and money. This chapter will guide you through the concepts of decimal place values, operations on decimals, and how to convert between fractions and decimals.

Key Concepts Covered:

1. What are Decimals?
   • A decimal is a way of expressing numbers that are not whole numbers, using a decimal point.
   • Example: In the number 2.5, 2 is the whole number, and 0.5 is the decimal part.
   • The decimal point separates the whole number part from the fractional part.
2. Place Value of Decimals:
   • Each place after the decimal point has a specific value:
     • Tenths (0.1), Hundredths (0.01), Thousandths (0.001), and so on.
   • Example: In the number 3.75, 3 is the whole number, 7 is in the tenths place, and 5 is in the hundredths place.
3. Comparing and Ordering Decimals:
   • To compare decimals, look at the digits from left to right:
     • If the whole number part is different, the larger whole number is greater.
     • If the whole numbers are the same, compare the digits in the decimal part.
   • Example: 0.8 is greater than 0.75 because 8 tenths is more than 7 tenths.
4. Converting Fractions to Decimals:
   • To convert a fraction to a decimal, divide the numerator by the denominator.
   • Example: $\frac{1}{2} = 0.5$21​=0.5.
5. Converting Decimals to Fractions:
   • To convert a decimal to a fraction, express the decimal as a fraction of 10, 100, or 1000, depending on the number of decimal places.
   • Example: 0.75 can be written as $\frac{75}{100}$10075​, which simplifies to $\frac{3}{4}$43​.
6. Addition and Subtraction of Decimals:
   • Addition: Align the decimal points and add as usual.
   • Subtraction: Align the decimal points and subtract as usual.
   • Example: $3.5 + 1.75 = 5.25$3.5+1.75=5.25.
7. Multiplication and Division of Decimals:
   • Multiplication: Multiply the numbers as if they were whole numbers, then count the total number of decimal places in both factors and place the decimal in the product accordingly.
   • Division: Move the decimal point in the divisor and dividend to make the divisor a whole number, then divide as usual.

Important Questions with Answers:

1. What is the decimal form of 34\frac{3}{4}43​?
   • Answer: 0.75.
2. Convert 0.6 into a fraction.
   • Answer: $\frac{6}{10} = \frac{3}{5}$106​=53​.
3. What is the sum of 5.3 and 2.65?
   • Answer: 7.95.
4. Compare 0.9 and 0.99. Which is greater?
   • Answer: 0.99 is greater because 99 hundredths is more than 90 hundredths.
5. Multiply: 0.4 × 0.3.
   • Answer: 0.12.
6. Subtract: 7.8 – 2.56.
   • Answer: 5.24.