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\ 08-Oct-2025 Bharat Arora Proof-9 Reader’s Sign _______________________ Date __________

2. Arrange the following numbers in ascending order.

( a) 863532, 8654627, 7825216, 7324545 (b) 5231761, 2000413, 2050009, 2500496
( c) 6954521, 6954544, 6954530, 6954524 (d) 75465421, 75464521, 75463211, 75463251

3. Arrange the following numbers in descending order.

( a) 87976, 76049, 75959, 97479 (b) 528781, 452678, 453170, 654675

( c) 798667, 7983678, 7893569, 9400045 (d) 9864542, 9864521, 98645321, 9865021

4. Find the smallest and the greatest numbers formed using the digits 0, 3, 7, 6, 8, 5
without repetition.
5. Write the smallest and the greatest 8-digit numbers using the digits 4, 0, 1, 7, 5, 6, 9,
8 without repetition.
6. Write the greatest and the smallest 7-digit numbers using the given digits with
repetition of digits.

( a) 5, 7, 2, 4, 0 (b) 7, 5, 9, 6 (c) 3, 2, 7, 0 (d) 5, 9, 3

internationaL PLace VaLue system

This is another place value system which is used to read and write numbers. This place value
system is commonly used globally. In this system, every period has three places. Let us take

the number 65423198 and place it in the international place value chart as shown below.
Periods Millions Thousands Ones
Places Hundred Ten Millions Hundred Ten Thousands Hundreds Tens Ones
Millions Millions (M) Thousands Thousands (Th) (H) (T) (O)
(HM) (TM) (HTh) (TTh)
100,000,000 10,000,000 1,000,000 100,000 10,000 1000 100 10 1

6 5 4 2 3 1 9 8

In this place value system, the names of the periods are Ones, Thousands, Millions, etc.
The ones period has three places: ones, tens and hundreds. The thousands period has
three places: thousands, ten thousands and hundred thousands. The millions period has
three places: millions, ten millions and hundred millions.

Let us read and write the number shown in the above place value chart.
In this number system, we put commas after every third digit from the right of the number

to separate the periods.
In words: Sixty-five million four hundred twenty-three thousand one hundred ninety-eight.

Using commas: 65, 423, 198

Millions Ones
period Thousands period
period

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