Decimals: CBSE Class 6 Maths NCERT Guide

What Are Decimals? A Look at Place Value

A decimal number has two parts: a whole number part and a decimal part, separated by a decimal point (.). The digits to the left of the decimal point are whole numbers we already know (ones, tens, hundreds). The digits to the right of the point represent parts of a whole.

The first digit after the decimal point is in the tenths place (1/10). The next digit is in the hundredths place (1/100), and the one after that is in the thousandths place (1/1000), and so on.

Let's take the number 37.45.

• The whole number part is 37 (3 tens and 7 ones).
• The decimal point separates the parts.
• The decimal part is 45.
• The digit '4' is in the tenths place, meaning it represents 4/10.
• The digit '5' is in the hundredths place, meaning it represents 5/100.

So, 37.45 is the same as 37 + 4/10 + 5/100. Understanding this place value is the key to working with decimals!

How to Convert Fractions to Decimals

1. Step 1: Check the Denominator — Look at the fraction's denominator (the bottom number). Our goal is to make it a power of 10 (like 10, 100, 1000, etc.).
2. Step 2: Convert the Denominator — Find a number to multiply the denominator by to make it 10, 100, or 1000. You MUST multiply the numerator (top number) by the same number. For example, to convert 2/5, we multiply the denominator 5 by 2 to get 10. So we must also multiply the numerator 2 by 2. This gives us the new fraction 4/10.
3. Step 3: Place the Decimal Point — Write down the new numerator (in our example, 4). Now, count the number of zeros in the denominator (10 has one zero). From the right side of the numerator, move the decimal point to the left by that many places. For 4/10, we move one place to get 0.4. For a fraction like 65/100, we move two places to get 0.65.

Worked Examples: Adding and Subtracting Decimals

• Example 1: Add 15.4 and 8.75 Step 1: Line up the decimal points. Write the numbers one below the other so the decimal points are in a straight vertical line. To make it easier, you can add a zero to 15.4 to make it 15.40. `` 15.40 + 8.75 ------- `` Step 2: Add from right to left. Add just like you do with whole numbers. - Hundredths column: 0 + 5 = 5 - Tenths column: 4 + 7 = 11. Write down 1 and carry over 1 to the ones place. - Ones column: 1 (carry-over) + 5 + 8 = 14. Write down 4 and carry over 1 to the tens place. - Tens column: 1 (carry-over) + 1 = 2. Step 3: Place the decimal point in the answer. The decimal point in the sum goes directly below the decimal points in the numbers you added. Final Answer: 24.15
• Example 2: Subtract 9.25 from 21.5 Step 1: Line up the decimal points. Write 21.5 and place 9.25 below it, keeping the decimal points aligned. Add a zero to 21.5 to make it 21.50. `` 21.50 - 9.25 ------- `` Step 2: Subtract from right to left. You can't subtract 5 from 0, so you need to borrow. - Borrow from the 5 in the tenths place. The 0 becomes 10, and the 5 becomes 4. In the hundredths column: 10 - 5 = 5. - In the tenths column: 4 - 2 = 2. - In the ones column, you can't subtract 9 from 1, so borrow from the 2 in the tens place. The 1 becomes 11 and the 2 becomes 1. Now, 11 - 9 = 2. - In the tens column: 1 - 0 = 1. Step 3: Place the decimal point in the answer. Final Answer: 12.25

Important Points: Avoid Common Mistakes with Decimals

• Align the Point: When adding or subtracting, ALWAYS line up the decimal points vertically. This is the most important rule. Misaligning the points is the most common error.
• Use Placeholder Zeros: Adding zeros to the end of the decimal part doesn't change the number's value (e.g., 7.5 is the same as 7.50). Use these 'placeholder' zeros to help you line up numbers neatly for addition and subtraction.
• Comparing Decimals: To compare numbers like 6.8 and 6.75, first check the whole number part (both are 6). Then, look at the tenths place. Since 8 is greater than 7, we know that 6.8 > 6.75.
• Reading Decimals: Remember that 0.9 is nine tenths, while 0.09 is nine hundredths. The position of the digit after the decimal point matters a lot!

Practice Questions with Solutions

• Q: Write the decimal number for "Forty-seven and six-hundredths". A: Step 1: Identify the whole number part. This is "Forty-seven", which is 47. Step 2: Identify the decimal part. "Six-hundredths" means 6 in the hundredths place. The hundredths place is the second digit after the decimal point. Step 3: Combine the parts. We write the whole number, then the decimal point. Since there are no tenths, we put a 0 in the tenths place, and then 6 in the hundredths place. Final answer: 47.06
• Q: Convert the fraction 3/4 into a decimal. A: Step 1: Our goal is to make the denominator (4) into 100. We know that 4 × 25 = 100. Step 2: To keep the fraction equivalent, we must multiply the numerator (3) by the same number. So, 3 × 25 = 75. Step 3: Our new fraction is 75/100. To write this as a decimal, we write the numerator 75 and move the decimal point two places to the left (because 100 has two zeros). Final answer: 0.75
• Q: Sunita traveled 15.25 km by bus, 7.08 km by auto, and 1.5 km on foot. What is the total distance she traveled? A: Step 1: To find the total distance, we need to add all three distances. Let's line them up by their decimal points. We can add zeros to make them all have two decimal places. `` 15.25 7.08 + 1.50 ------- `` Step 2: Add the numbers column by column from right to left. - Hundredths: 5 + 8 + 0 = 13 (Write 3, carry over 1) - Tenths: 1 (carry-over) + 2 + 0 + 5 = 8 - Ones: 5 + 7 + 1 = 13 (Write 3, carry over 1) - Tens: 1 (carry-over) + 1 = 2 Step 3: Place the decimal point in the answer directly below the others. Final answer: Sunita traveled a total of 23.83 km.
• Q: Which is greater: 5.607 or 5.67? A: Step 1: Compare the whole number parts. Both numbers have 5 as the whole number part, so they are equal so far. Step 2: Compare the digits in the tenths place. Both numbers have 6 in the tenths place, so they are still equal. Step 3: Compare the digits in the hundredths place. The first number has 0, and the second number has 7. Since 7 is greater than 0, the second number is greater. Final answer: 5.67 is greater than 5.607.

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