Problem 20 - Fundamentals of Mathematics

Question

Is there a smallest two digit number? If so, what is it?

Step-by-Step Solution

Answer

The smallest two-digit number is 10.

Step 1: Define Two-Digit Number

Two-digit numbers are numbers that consist of two numerical digits, ranging from 10 to 99.

Step 2: Identify the Smallest Number

Since two-digit numbers begin at the smallest possible two-digit combination, we need to determine the smallest number among the two-digit numbers.

Step 3: Conclusion

The smallest number with two digits is 10, as it is the first number that fulfills the two-digit criteria, starting from the lowest possible value.

Key Concepts

Number Range

When we talk about two-digit numbers, we are referring to numbers that have exactly two digits. These numbers range from 10 to 99. Each number within this range is unique because of its two distinct places: the tens place and the units place.

It's important to note that before 10 is the number 9, which is a single-digit number. Therefore, 10 is where two-digit numbers start. On the upper end, 99 is the highest two-digit number before transitioning into the hundreds category with 100. Understanding the number range helps in recognizing where two-digit numbers sit in the broader spectrum of numerical values.

Smallest Number

The smallest number in the range of two-digit numbers is 10. Here's why:

• A two-digit number must have digits in both the tens and units place.
• In the number 10, the digit '1' is in the tens place, making it the smallest possible tens digit with a number in the ones place.
• The number 10 is the first in the sequence that meets the two-digit criteria, making it the smallest.

By grasping this concept, you understand that to be a two-digit number, a number needs to be greater than any single-digit number, making 10 the starting point of this category.

Place Value

Place value is a fundamental concept in understanding the two-digit numbers. It explains the role of each digit in a number based on its position. For instance, in the number 10:

• The '1' is in the tens place. This means it represents 10, showing that it contributes a multiple of ten to the overall value of the number.
• The '0' is in the units place. This means it contributes nothing beyond the ten, which is why 10 is represented simply as 10 + 0.

By applying place value, you can break down a number like 73 as being 7 tens and 3 units. Understanding place value is crucial for not just identifying numbers but also for performing arithmetic operations such as addition and subtraction.