CBSE Class 4 Mathematics Numbers up to 10,000 Place Value and Comparison Notes Set 01

Reading and writing numbers up to 10,000

We can write a number in figures or in words. The smallest 4-digit number is 1000 and the largest is 9999. When we add 1 to 9999 we get 10,000, which is read as ten thousand. Examples: 4,507 is four thousand five hundred seven, and 9,090 is nine thousand ninety.

Place value chart

Each digit has a place: ones (O), tens (T), hundreds (H) and thousands (Th), moving from right to left. Ten ones make one ten, ten tens make one hundred and ten hundreds make one thousand.

Face value and place value

The face value of a digit is the digit itself, wherever it is. The place value of a digit is its face value multiplied by the value of its place. In 7,293 the digit 2 has face value 2 and place value 2 × 100 = 200. The place value of 0 is always 0.

Expanded form

A number can be broken into the place values of its digits. For example, 6,308 = 6000 + 300 + 0 + 8 = 6000 + 300 + 8. Writing the sum back as one number is called the short form.

Successor and predecessor

The successor of a number is the number just after it (one more). The predecessor is the number just before it (one less). The successor of 8,999 is 9,000. The predecessor of 1,000 is 999.

Comparing and ordering numbers

1. A number with more digits is greater.
2. If the number of digits is equal, compare the digits from the left. The first place where they differ decides the answer.
3. Ascending order means smallest to greatest. Descending order means greatest to smallest.
For example, 5,429 and 5,492: thousands and hundreds are equal, but in the tens place 2 is less than 9, so 5,429 is less than 5,492.

Forming numbers from given digits

To make the smallest number, put the digits in ascending order (taking care that the first digit is not 0). To make the greatest number, put them in descending order. Using 5, 2 and 6 once each, the smallest 3-digit number is 256 and the greatest is 652.

Skip counting

Counting with a fixed gap between numbers is skip counting. Counting by fives from 2,715 gives 2,715, 2,720, 2,725, 2,730. Counting by hundreds from 4,650 gives 4,650, 4,750, 4,850.

Key points

1. Place values from right to left: ones, tens, hundreds, thousands.
2. Place value = face value × value of the place.
3. Successor = number + 1; predecessor = number − 1.
4. Compare digit by digit from the left.

Worked examples

Example 1. Write 7,056 in expanded form. Answer: 7000 + 0 + 50 + 6 = 7000 + 50 + 6.

Example 2. Arrange 4,382; 4,328; 3,842 in descending order. Answer: 3,842 has the smallest thousands digit, so it is last. Between 4,382 and 4,328 the hundreds are equal (3), then 8 tens is more than 2 tens. The order is 4,382; 4,328; 3,842.

Example 3. Find the difference between the place values of 8 and 5 in 8,152. Answer: place value of 8 is 8000 and of 5 is 50. The difference is 8000 − 50 = 7950.

Quick Check Questions