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

Description: This quiz explores the fundamental role of zero in the decimal system, a cornerstone of modern arithmetic. Test your understanding of zero's significance and its impact on mathematical operations.
Number of Questions: 14
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Tags: zero decimal system place value arithmetic
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In the decimal system, the value of a digit depends on its position. What is the value of the digit '5' in the number 532?

  1. 5

  2. 50

  3. 500

  4. 5000


Correct Option: B
Explanation:

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.

What is the place value of the digit '3' in the number 3456?

  1. 3

  2. 30

  3. 300

  4. 3000


Correct Option: C
Explanation:

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. What does this mean?

  1. It uses 10 digits (0-9) to represent numbers.

  2. It groups digits into sets of 10.

  3. It uses powers of 10 to determine the value of digits.

  4. All of the above


Correct Option: D
Explanation:

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.

Which of the following numbers is written correctly in expanded form?

  1. 345 = 300 + 40 + 5

  2. 789 = 700 + 80 + 9

  3. 1234 = 1000 + 200 + 30 + 4

  4. 9876 = 9000 + 800 + 70 + 6


Correct Option: C
Explanation:

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.

What is the role of zero in the decimal system?

  1. It represents an empty set.

  2. It holds a place value.

  3. It allows for the representation of negative numbers.

  4. All of the above


Correct Option: D
Explanation:

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.

In the number 2045, what is the value of the digit '0'?

  1. 0

  2. 10

  3. 100

  4. 1000


Correct Option: A
Explanation:

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.

Which of the following numbers is the largest?

  1. 3456

  2. 4567

  3. 5678

  4. 6789


Correct Option: D
Explanation:

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.

What is the smallest 4-digit number that can be formed using the digits 1, 2, 3, and 4?

  1. 1234

  2. 1324

  3. 1423

  4. 2134


Correct Option: A
Explanation:

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.

Which of the following numbers is divisible by 5?

  1. 123

  2. 234

  3. 345

  4. 456


Correct Option: C
Explanation:

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.

What is the sum of the digits in the number 7894?

  1. 18

  2. 27

  3. 36

  4. 45


Correct Option:
Explanation:

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

Which of the following numbers is the product of its digits?

  1. 123

  2. 234

  3. 345

  4. 456


Correct Option: A
Explanation:

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.

What is the difference between the greatest and smallest 3-digit numbers that can be formed using the digits 2, 5, and 8?

  1. 432

  2. 456

  3. 564

  4. 654


Correct Option: A
Explanation:

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.

Which of the following numbers is a multiple of 3?

  1. 123

  2. 234

  3. 345

  4. 456


Correct Option: C
Explanation:

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.

What is the value of the expression (3 + 4) x (5 - 2)?

  1. 11

  2. 13

  3. 15

  4. 17


Correct Option: C
Explanation:

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.

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