GSEB Class 6 Maths Solutions Chapter 8 Decimals Exercise 8.3

Question 1. Which is greater?
(a) 0.3 or 0.4
(b) 0.07 or 0.02
(c) 3 or 0.8
(d) 0.5 or 0.05
(e) 1.23 or 1.2
(f) 0.099 or 0.19
(g) 1.5 or 1.50
(h) 1.431 or 1.490
(i) 3.3 or 3.300
(j) 5.64 or 5.603
Answer:
(a) 0.3 or 0.4
Since \( 0.3 = \frac { 3 }{ 10 } \) and \( 0.4 = \frac { 4 }{ 10 } \).
\[ \frac { 3 }{ 10 } < \frac { 4 }{ 10 } \]
\( \implies \) So, \( 0.3 < 0.4 \).
Therefore, 0.4 is a larger number than 0.3.
(b) 0.07 or 0.02
Since \( 0.07 = \frac { 7 }{ 100 } \) and \( 0.02 = \frac { 2 }{ 100 } \).
\[ \frac { 7 }{ 100 } > \frac { 2 }{ 100 } \]
\( \implies \) So, \( 0.07 > 0.02 \).
Therefore, 0.07 is a larger number than 0.02.
(c) 3 or 0.8
Since 3 is greater than 0, it means that 3 is also greater than 0.8.
Therefore, 3 is the larger number compared to 0.8.
(d) 0.5 or 0.05
Since \( 0.05 = \frac { 5 }{ 100 } \) which is equal to \( \frac { 50 }{ 100 } \).
And \( 0.5 = \frac { 5 }{ 10 } \) which is also equal to \( \frac { 50 }{ 100 } \).
\[ \frac { 50 }{ 100 } > \frac { 5 }{ 100 } \]
\( \implies \) So, \( 0.5 > 0.05 \).
Thus, 0.5 is a larger number than 0.05.
(e) 1.23 or 1.2
Since \( 1.23 = \frac { 123 }{ 100 } \).
And \( 1.2 = \frac { 12 }{ 10 } \) which is equal to \( \frac { 120 }{ 100 } \).
\[ \frac { 123 }{ 100 } > \frac { 120 }{ 100 } \]
\( \implies \) So, \( 1.23 > 1.2 \).
Thus, 1.23 is a larger number than 1.2.
(f) 0.099 or 0.19
Since \( 0.099 = \frac { 99 }{ 1000 } \).
And \( 0.19 = \frac { 19 }{ 100 } \) which is equal to \( \frac { 190 }{ 1000 } \).
\[ \frac { 190 }{ 1000 } > \frac { 99 }{ 1000 } \]
\( \implies \) So, \( 0.19 > 0.099 \).
Thus, 0.19 is a larger number than 0.099.
(g) 1.5 or 1.50
Since \( 1.5 = \frac { 15 }{ 10 } \) which is equal to \( \frac { 150 }{ 100 } \).
And \( 1.50 = \frac { 150 }{ 100 } \).
\[ \frac { 150 }{ 100 } = \frac { 150 }{ 100 } \]
\( \implies \) So, \( 1.5 = 1.50 \).
Thus, 1.5 and 1.50 are the same value.
(h) 1.431 or 1.490
Since \( 1.431 = \frac { 1431 }{ 1000 } \).
And \( 1.490 = \frac { 1490 }{ 1000 } \).
\[ \frac { 1490 }{ 1000 } > \frac { 1431 }{ 1000 } \]
\( \implies \) So, \( 1.490 > 1.431 \).
Thus, 1.490 is a larger number than 1.431.
(i) 3.3 or 3.300
Since \( 3.3 = \frac { 33 }{ 10 } \) which is equal to \( \frac { 3300 }{ 1000 } \).
And \( 3.300 = \frac { 3300 }{ 1000 } \).
\[ \frac { 3300 }{ 1000 } = \frac { 3300 }{ 1000 } \]
\( \implies \) So, \( 3.3 = 3.300 \).
Thus, 3.3 and 3.300 are the same value.
(j) 5.64 or 5.603
Since \( 5.64 = \frac { 564 }{ 100 } \) which is equal to \( \frac { 5640 }{ 1000 } \).
And \( 5.603 = \frac { 5603 }{ 1000 } \).
\[ \frac { 5640 }{ 1000 } > \frac { 5603 }{ 1000 } \]
\( \implies \) So, \( 5.64 > 5.603 \).
Thus, 5.64 is a larger number than 5.603.
In simple words: To find which decimal is bigger, compare their digits from left to right. You can add zeros to the end of a decimal without changing its value to make them have the same number of decimal places, which makes comparison easier.

Exam Tip: When comparing decimals, always align the decimal points and then compare digits from left to right, starting with the highest place value. Adding trailing zeros to match the number of decimal places can help prevent errors.

Question 2. Make five more examples and find the greater number from them.
Answer: Examples to find which is greater:
(i) 1.09 or 1.092
(ii) 1.0 or 0.99
(iii) 23.55 or 23.5<
(iv) 3.03 or 3.30
(v) 10.12 or 10.21
Here, we discover that:
(i) 1.092
(ii) 1.0
(iii) 23.55
(iv) 3.30
(v) 10.21
These are the larger decimals in each pair.
In simple words: We create new pairs of decimal numbers and then decide which one is larger for each pair.

Exam Tip: When creating examples, ensure they clearly illustrate the concept being tested. For comparing decimals, make sure some pairs differ in the tenths place, others in the hundredths, and so on, to show full understanding.