Decimals Ex 8.3 Class 6 NCERT Solutions & Concepts

Understanding How to Compare Decimals

When we compare whole numbers like 45 and 302, it is easy to see that 302 is larger because it has more digits. However, decimals can be tricky! For example, is 0.07 greater than 0.1? At first glance, a student might see '7' and think 0.07 is larger than 0.1 because 7 is greater than 1. But this is a common trap! To compare decimals accurately, we must compare the digits at corresponding place values starting from the left. First, compare the whole number parts. If they are equal, move to the tenths place (1/10). If those are also equal, move to the hundredths place (1/100), and then the thousandths place (1/1000). We can also make comparisons easier by writing extra zeros at the end of a decimal to make them 'like decimals' with the same number of decimal places without changing their actual value.

The Step-by-Step Method to Compare Decimals

1. Identify the Whole Number Parts — Look at the digits to the left of the decimal point. The number with the larger whole number part is always greater. For example, 5.2 is greater than 3.9 because 5 is greater than 3.
2. Compare the Tenths Digit — If the whole number parts are equal, compare the digits in the tenths place (the first digit to the right of the decimal point). For example, 0.5 is greater than 0.4 because 5 is greater than 4.
3. Compare the Hundredths Digit — If the tenths digits are also equal, move to the hundredths place. For example, with 0.19 and 0.12, both have 1 in the tenths place, but 9 is greater than 2, so 0.19 is greater than 0.12.
4. Convert to Like Decimals — If the decimals have different lengths, add placeholder zeros to the right of the last digit. For example, to compare 1.5 and 1.50, write 1.5 as 1.50. Now they look identical, which means they are equal: 1.5 = 1.50.

Worked Examples from NCERT Exercise 8.3

• Example 1: Compare 0.3 and 0.4. Which is greater? Step 1: Compare the whole number parts. Both have 0 as the whole number. Step 2: Compare the tenths place. The tenths digit of 0.3 is 3, and for 0.4 is 4. Step 3: Since 4 > 3, we can confidently say that 0.4 is greater than 0.3.
• Example 2: Which is greater: 0.07 or 0.02? Step 1: Whole number parts are both 0. Step 2: Tenths place digits are both 0. Step 3: Move to the hundredths place. The digit for 0.07 is 7, and for 0.02 is 2. Since 7 > 2, 0.07 is greater than 0.02.
• Example 3: Compare 1.5 and 1.50. Which is greater? Step 1: The whole numbers are both 1. Step 2: The tenths digits are both 5. Step 3: Convert 1.5 into a 'like decimal' by adding a zero at the end: 1.5 becomes 1.50. Step 4: Since both numbers are represented as 1.50, they are equal. Both are equal.

Exam Tip: Beware the 'More Digits' Trap!

A very common mistake in CBSE exams is thinking that a decimal with more digits is automatically larger. For example, students often write that $0.095$ is greater than $0.1$ because 95 is a bigger number than 1. This is incorrect! Remember to write them as like decimals first. If we make them have the same number of decimal places, $0.1$ becomes $0.100$. Now, compare $0.100$ and $0.095$. In the tenths place, $1$ is greater than $0$. Thus, $0.1 > 0.095$. Always align place values before deciding!

Practice Questions with Solutions

• Q: Which is greater: 3 or 0.8? A: Step 1: Write both numbers with a decimal point to make them easy to compare. 3 can be written as 3.0, and the other number is 0.8. Step 2: Compare the whole number parts. The whole number part of 3.0 is 3, and the whole number part of 0.8 is 0. Step 3: Since 3 > 0, the number 3 is greater. Final answer: 3 is greater than 0.8.
• Q: Which is greater: 0.5 or 0.05? A: Step 1: Make them like decimals by adding a zero to 0.5 so both have two decimal places. 0.5 becomes 0.50. Step 2: Now compare 0.50 and 0.05. Step 3: Look at the tenths place. 0.50 has 5 in the tenths place, while 0.05 has 0 in the tenths place. Step 4: Since 5 > 0, 0.50 is greater than 0.05. Final answer: 0.5 is greater than 0.05.
• Q: Which is greater: 1.431 or 1.490? A: Step 1: Compare the whole number parts. Both have 1 as their whole number. Step 2: Compare the tenths place. Both have 4 in the tenths place. Step 3: Compare the hundredths place. 1.431 has 3 in the hundredths place, while 1.490 has 9 in the hundredths place. Step 4: Since 9 > 3, 1.490 is greater than 1.431. Final answer: 1.490 is greater than 1.431.
• Q: Which is greater: 5.64 or 5.603? A: Step 1: Make them like decimals. 5.64 has two decimal places, and 5.603 has three decimal places. Add a zero to 5.64 to get 5.640. Step 2: Compare 5.640 and 5.603. The whole numbers are both 5. Step 3: The tenths digits are both 6. Step 4: Compare the hundredths digits. 5.640 has 4 in the hundredths place, while 5.603 has 0 in the hundredths place. Step 5: Since 4 > 0, 5.640 is greater. Final answer: 5.64 is greater than 5.603.

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