Exploring the Role of Zero in the Decimal System: A Foundation of Modern Arithmetic

In the decimal system, the value of a digit is determined by its place value. In the number 532, the digit '5' is in the tens place, so its value is 50.

The place value of a digit indicates the value it represents based on its position in a number. In the number 3456, the digit '3' is in the hundreds place, so its place value is 300.

The decimal system is a base-10 system, which means it uses 10 digits (0-9) to represent numbers. It groups digits into sets of 10 and uses powers of 10 to determine the value of digits.

Expanded form represents a number as the sum of its individual digits multiplied by their respective place values. The correct expanded form for 1234 is 1000 + 200 + 30 + 4.

Zero plays a crucial role in the decimal system. It represents an empty set, holds a place value, and enables the representation of negative numbers.

The digit '0' in the number 2045 holds the place value of the tens. However, since there is no digit in the tens place, its value is 0.

To determine the largest number, compare the digits from left to right. Since 6 is greater than 3, 4, and 5, the largest number is 6789.

To form the smallest 4-digit number, arrange the digits in ascending order from left to right. Therefore, the smallest 4-digit number is 1234.

A number is divisible by 5 if its last digit is either 0 or 5. In this case, 345 is the only number with a last digit of 5, so it is divisible by 5.

To find the sum of the digits, add the individual digits of the number. 7 + 8 + 9 + 4 = 28.

The product of the digits of a number is found by multiplying all its digits together. In this case, 1 x 2 x 3 = 6, so 123 is the only number whose digits multiply to give 6.

To find the greatest 3-digit number, arrange the digits in descending order (852), and for the smallest, arrange them in ascending order (258). The difference between 852 and 258 is 432.

A number is a multiple of 3 if the sum of its digits is divisible by 3. In this case, 3 + 4 + 5 = 12, which is divisible by 3, so 345 is a multiple of 3.

First, evaluate the parentheses: (3 + 4) = 7 and (5 - 2) = 3. Then, perform the multiplication: 7 x 3 = 21. Therefore, the value of the expression is 21.