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Numbers up to 10,000 - Comparing and Ordering Numbers

Grade 3ICSE

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

🔑Concepts

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Comparing Numbers with Different Digits: A number with more digits is always greater than a number with fewer digits. For example, 1,0001,000 (a 4-digit number) is greater than 999999 (a 3-digit number). Visually, you can imagine a 4-column place value chart compared to a 3-column chart; the 4-column chart has a value in the Thousands place while the other is empty.

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Comparing Numbers with the Same Number of Digits: To compare two 4-digit numbers, start by comparing the digits in the Thousands place. If they are the same, compare the Hundreds place, then the Tens place, and finally the Ones place. Imagine two stacks of blocks representing the numbers; you check the largest blocks (Thousands) first to see which stack is taller.

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Comparison Symbols: We use specific symbols to show the relationship between two numbers: >> (Greater Than), << (Less Than), and == (Equal To). A helpful visual is to think of the symbol as an alligator's mouth that always opens wide to 'eat' the larger number.

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Ascending Order: This means arranging numbers from the smallest to the greatest. Visually, this is like climbing up a ladder or a staircase where each step represents a larger number value.

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Descending Order: This means arranging numbers from the greatest to the smallest. Imagine walking down a staircase or sliding down a slide, where you start at the highest value and move toward the lowest.

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Successor and Predecessor: The successor is the number that comes immediately after a given number (+1+1), while the predecessor is the number that comes immediately before it (−1-1). On a horizontal number line, the successor is one step to the right, and the predecessor is one step to the left.

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Forming Numbers from Digits: To form the greatest 4-digit number using four given digits, arrange the digits in descending order (largest to smallest). To form the smallest number, arrange them in ascending order (smallest to largest). If one digit is 00, place it in the second position from the left (Hundreds place) because a 4-digit number cannot start with 00.

📐Formulae

Successor=Number+1Successor = Number + 1

Predecessor=Number−1Predecessor = Number - 1

a>b if a is greater than ba > b \text{ if } a \text{ is greater than } b

a<b if a is less than ba < b \text{ if } a \text{ is less than } b

a=b if a is equal to ba = b \text{ if } a \text{ is equal to } b

💡Examples

Problem 1:

Compare the numbers 4,5824,582 and 4,5394,539 using the correct symbol (>>, <<, or ==).

Solution:

Step 1: Compare the Thousands place. Both numbers have 44 in the thousands place (4,000=4,0004,000 = 4,000). Step 2: Compare the Hundreds place. Both numbers have 55 in the hundreds place (500=500500 = 500). Step 3: Compare the Tens place. The first number has 88 (8080) and the second number has 33 (3030). Step 4: Since 8>38 > 3, it follows that 4,582>4,5394,582 > 4,539.

Explanation:

When the higher place values (thousands and hundreds) are identical, we look at the next place value (tens) to determine which number is larger.

Problem 2:

Arrange the following numbers in ascending order: 3,210,3,021,3,201,2,9993,210, 3,021, 3,201, 2,999.

Solution:

Step 1: Identify the number of digits. All are 4-digit numbers. Step 2: Compare the Thousands place. 2,9992,999 has a 22, while the others have 33. So, 2,9992,999 is the smallest. Step 3: Compare the Hundreds place for the remaining numbers (3,210,3,021,3,2013,210, 3,021, 3,201). 3,0213,021 has 00 hundreds, so it is the next smallest. Step 4: Compare the Tens place for 3,2103,210 and 3,2013,201. 3,2013,201 has 00 tens and 3,2103,210 has 11 ten. So, 3,201<3,2103,201 < 3,210. Step 5: The final order is 2,999<3,021<3,201<3,2102,999 < 3,021 < 3,201 < 3,210.

Explanation:

Ascending order requires moving from the smallest value to the largest value by checking place values from left to right.