Problem 106 - Fundamentals of Mathematics

Question

Write a three-digit number that has a zero in the ones position.

Step-by-Step Solution

Answer

250 is a valid choice.

Step 1: Understand the requirement

We need to write a three-digit number where the ones place is occupied by zero. This means the number will look like ABC0, where A, B, and C represent digits.

Step 2: Analyze the range of possible values

The number must be three-digit, which means A can range from 1 to 9 (to ensure the number is three digits) and B and C can be any digit from 0 to 9. As per the problem, the ones digit is 0.

Step 3: Choose example digits

Select A = 2, B = 5, and C = 4 as an example. Thus, the number ABC0 turns into 250.

Key Concepts

Place Value

Understanding place value is crucial when working with three-digit numbers. Each digit in a number has a specific place value, which determines its value based on its position. In a three-digit number, the three positions are:

• The hundreds place.
• The tens place.
• The ones place.

For example, in the number 250, the digit '2' is in the hundreds place, which means it represents 200, because 2 multiplied by 100 is 200. The digit '5' is in the tens place, which means it represents 50, as 5 times 10 equals 50. Finally, the '0' is in the ones place, indicating no additional units. Understanding this structure is very important, especially when solving the exercise of writing a number with specific digits in one or more places.

Number Construction

Constructing a number, especially a three-digit number, involves understanding the rules of digit placements and how these placements affect the overall value. When faced with a problem like creating a three-digit number with a particular requirement, such as a zero in the ones place, you must consider:

• The number of digits that can occupy each place: hundred (1-9), tens (0-9), and ones (which is fixed as 0 in this exercise).
• The order in which these digits are arranged to make a valid number.

For instance, when we decided on the digits 2, 5, and 0, we ensured the number maintains its integrity as a three-digit number. The hundreds digit '2' confirmed it's a three-digit number, and the tens digit '5' contributed to giving the number its value. Placing zero in the ones spot satisfied the condition, resulting in the number 250.

Problem Solving

Problem solving in mathematics often involves analyzing the requirements and constraints, then using logical reasoning to arrive at a solution. For the exercise of writing a three-digit number with zero in the ones place, the steps include:

• Understanding what is specifically required: a three-digit format with zero at the end.
• Knowing how to fill the hundreds and tens places satisfactorily.
• Choosing suitable digits that meet all conditions and constraints, such as a number like 250.

By breaking down the task and considering each positional requirement one at a time, you learn to approach similar problems methodically. The essence of problem solving here is to ensure compliance with all given constraints while creatively selecting values that fit within those boundaries. This approach not only provides a solution but also improves your ability to tackle diverse mathematical problems.