 # IMO Class 4 Chapter 1: Number System

A Math Olympiad is a competition that tests mathematical skills and abilities of students. The International Mathematical Olympiad (IMO) is the largest and most prestigious Math Olympiad in the world, and it is held annually for high school students.

Participating in Math Olympiads can be a great opportunity for students to develop their mathematical abilities, problem-solving skills, and critical thinking. It can also help them to build confidence and teamwork skills as they work with other students to solve challenging problems.

Many students who participate in Math Olympiads go on to study mathematics, science, engineering, or other related fields in college. In addition to academic benefits, Math Olympiad tests can also help students develop important life skills such as time management, perseverance, and teamwork.

By working together to solve complex mathematical problems, students can learn how to collaborate effectively and communicate their ideas clearly, which are skills that can benefit them throughout their lives.

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## IMO Class 4 Chapter 1: Number System

Math in grade 4 focuses on six-digit numbers. Students learn to read and write numbers up to one million, understand the place value of digits within a number, compare and order numbers, and round numbers to the nearest ten, hundred, or thousand.

They also learn how to add and subtract six-digit numbers using both mental strategies and written methods, such as column addition and subtraction. Multiplication and division facts are reinforced, and students begin to work with larger numbers using written methods.

### Place Value of 6-digit numbers

Write 654213 in expanded form, for instance.

The expanded form of 654213 is: 600000 + 50000 + 4000 + 200 + 10 + 3

### Contrasting Two Numbers

To contrast two six-digit numbers, we follow these guidelines:

1. Start by comparing the number of digits in each number. If one number has more digits than the other, it is greater than the other number. For example, 123456 is greater than 1234.
2. If both numbers have the same number of digits, compare the leftmost digit of each number. The number with the greater leftmost digit is greater than the other number. For example, 345678 is greater than 234567.
3. If the leftmost digits of both numbers are the same, compare the next digit to the right of each number. Continue comparing digits to the right until you find two digits that are different. The number with the larger digit is greater than the other number. For example, 456789 is greater than 456788.
4. If all the digits of the two numbers are the same, then the numbers are equal. For example, 123456 is equal to 123456.

By following these guidelines, we can compare and contrast two six-digit numbers and determine which number is greater or if they are equal.

Which number, for instance, is larger? 885785 and 856865

Answer: To compare the two numbers 885785 and 856865, we can follow the guidelines for contrasting two six-digit numbers:

1. Both numbers have six digits, so we compare their left-most digits. The left-most digit of 885785 is 8, and the left-most digit of 856865 is also 8.
2. Since the left-most digits are the same, we compare the next digit to the right. The digit to the right of 8 in 885785 is 8, and the digit to the right of 8 in 856865 is 5. Since 8 is greater than 5, we can conclude that 885785 is greater than 856865.

Therefore, the larger number between 885785 and 856865 is 885785.

### Ascending Order

Ascending order means arranging the numbers from the smallest to the largest, while descending order means arranging the numbers from the largest to the smallest.

Here’s an example of arranging three six-digit numbers in ascending and descending order:

Numbers to arrange: 234567, 125789, 458912

Ascending Order:

1. Start by comparing the left-most digit of each number. The smallest left-most digit is 1, so the number 125789 should come first.
2. Next, compare the next digit to the right of each number. The next smallest digit is 2, so 234567 should come next.
3. Finally, 458912 has the largest left-most digit, so it should come last.

Therefore, the numbers arranged in ascending order are: 125789, 234567, 458912.

### Decreasing Order

1. Start by comparing the left-most digit of each number. The largest left-most digit is 4, so the number 458912 should come first.
2. Next, compare the next digit to the right of each number. The next largest digit is 5, so 234567 should come next.
3. Finally, 125789 has the smallest left-most digit, so it should come last.

Therefore, the numbers arranged in descending order are: 458912, 234567, 125789.

1. The IMO encourages the development of problem-solving and critical thinking skills in students.
2. Participating in the IMO can help students improve their mathematical abilities and performance in other academic subjects.
3. The IMO provides opportunities for students to showcase their talents and compete against peers from around the world.
4. Preparing for the IMO can foster a love for learning and a passion for mathematics in students.
5. The IMO can open doors to future academic and professional opportunities in fields such as mathematics, science, engineering, and technology.

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