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Knowing Our Numbers - Comparing Numbers

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Rule 1: If two numbers have a different number of digits, the number with more digits is the greater number. For example, a 55-digit number is always greater than a 44-digit number.

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Rule 2: If two numbers have the same number of digits, we compare the digits starting from the leftmost place (the highest place value).

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Rule 3: If the leftmost digits are the same, we compare the next digits to the right, and continue this process until we find digits that are different.

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Ascending Order: Arranging numbers from the smallest to the greatest. This can be represented as n1<n2<n3<⋯<nkn_1 < n_2 < n_3 < \dots < n_k.

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Descending Order: Arranging numbers from the greatest to the smallest. This can be represented as n1>n2>n3>⋯>nkn_1 > n_2 > n_3 > \dots > n_k.

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Place Value Comparison: When comparing large numbers, use the Indian Place Value system (Lakhs, Crores) or the International Place Value system (Millions, Billions) to align digits correctly.

📐Formulae

Digits in A>Digits in B  ⟹  A>B\text{Digits in } A > \text{Digits in } B \implies A > B

Place Value=Face Value×Position Value\text{Place Value} = \text{Face Value} \times \text{Position Value}

Comparison Symbol: > (Greater Than), < (Less Than), = (Equal To)\text{Comparison Symbol: } > \text{ (Greater Than), } < \text{ (Less Than), } = \text{ (Equal To)}

💡Examples

Problem 1:

Compare the numbers 92,34592,345 and 1,02,3451,02,345.

Solution:

92,345<1,02,34592,345 < 1,02,345

Explanation:

The first number 92,34592,345 has 55 digits, while the second number 1,02,3451,02,345 has 66 digits. According to Rule 1, a number with more digits is greater. Therefore, 1,02,3451,02,345 is greater.

Problem 2:

Compare 7,56,4327,56,432 and 7,56,7897,56,789.

Solution:

7,56,432<7,56,7897,56,432 < 7,56,789

Explanation:

Both numbers have 66 digits. We compare from the left: Lakhs place (7=77=7), Ten-thousands place (5=55=5), Thousands place (6=66=6). At the Hundreds place, 4<74 < 7. Thus, 7,56,4327,56,432 is smaller.

Problem 3:

Arrange the following numbers in Ascending Order: 45,67845,678, 45,12345,123, 45,90045,900, 45,00545,005.

Solution:

45,005<45,123<45,678<45,90045,005 < 45,123 < 45,678 < 45,900

Explanation:

All numbers have 55 digits and start with 4545. Comparing the hundreds place: 0<1<6<90 < 1 < 6 < 9. Arranging them from smallest to greatest gives the ascending sequence.