CLASS-1
COMPARING BIGGER & SMALLER NUMBER

Comparing Bigger & Smaller Number –

Comparing the smallest and biggest numbers is a common mathematical concept that helps us understand the relative magnitudes of different numbers. It is essential in various fields, including mathematics, computer science, physics, and everyday life. Here are some key points about comparing the smallest and biggest numbers:

  1. Order of Numbers: Numbers can be ordered based on their magnitudes. When we compare two numbers, we can determine which one is greater, which one is smaller, or if they are equal.
  2. Real Numbers: In the set of real numbers, there is no largest or smallest number. As mentioned earlier, the concept of infinity represents a value larger than any real number, and negative infinity represents a value smaller than any real number. So, while we can compare specific real numbers, there is no single largest or smallest real number.
  3. Infinity (∞): In mathematics, infinity (∞) is used to represent an unbounded quantity or a value that has no upper or lower limit. It is not a specific number but rather a concept. For example, as you count up from any real number, you can keep adding 1 and never reach a "largest" number because there is always a larger number.
  4. Real Number Line: The real number line is a graphical representation of real numbers, where numbers are placed in order from left to right. The smallest numbers are on the left, and the largest numbers are on the right. Infinity is represented by arrows at both ends of the number line.
  5. Practical Comparisons: In practical applications, we often encounter large and small numbers. For example, when dealing with data in computer science, we might encounter very large numbers in cryptography or very small numbers in scientific notation for extremely small quantities.
  6. Notation: In mathematical notation, symbols like "<" (less than), ">" (greater than), "<=" (less than or equal to), and ">=" (greater than or equal to) are used to compare numbers.
  7. Exponents: In scientific notation, numbers are written in the form of a x 10^n, where "a" is a number greater than or equal to 1 and less than 10, and "n" is an integer representing the exponent. The exponent "n" indicates the number of places the decimal point should be moved to get the original number.

Overall, comparing the smallest and biggest numbers is an integral part of mathematics and has numerous applications in various fields. It helps us understand the relative sizes of numbers and their significance in different contexts.

Comparing the smallest and biggest numbers is a fundamental concept in mathematics and computer science. It involves determining the relative magnitudes of different numbers and understanding their order.

  1. Comparing Integers: In the context of integers (whole numbers), you can use the concepts of greater than (>), less than (<), greater than or equal to (>=), less than or equal to (<=), and equal to (==) to compare two numbers. For example:
  • 5 > 3    (5 is greater than 3)
  • 7 < 10  (7 is less than 10)
  • 4 >= 4  (4 is greater than or equal to 4)
  • 2 <= 2  (2 is less than or equal to 2)
  • 6 == 6  (6 is equal to 6)
  1. Comparing Real Numbers: When working with real numbers (numbers with decimal points), you can still use the same comparison operators as with integers. For example:
  • 3.14 > 2.71   (3.14 is greater than 2.71)
  • 0.5 < 1.0       (0.5 is less than 1.0)
  • 1.414 >= 1.414 (1.414 is greater than or equal to 1.414)
  • 0.2 <= 0.2     (0.2 is less than or equal to 0.2)
  • 5.5 == 5.5     (5.5 is equal to 5.5)
  1. Order of Magnitude: Comparing large numbers can involve considering their order of magnitude. The order of magnitude is the power of 10 to which a number is approximately equal. For example, 1,000 (10^3) is one order of magnitude larger than 100 (10^2) and three orders of magnitude larger than 1 (10^0).
  2. Minima and Maxima: In mathematics, you might also encounter concepts related to finding the minimum (smallest) and maximum (largest) values within a set of numbers or a function. For instance, finding the minimum and maximum values of a function can help identify its peak and valley points.
  3. Absolute Value: The absolute value of a number is its distance from zero on the number line, always represented as a positive value. Comparing the absolute values of two numbers allows you to determine which one is farther from zero.

Understanding how to compare the smallest and biggest numbers is crucial in various real-world applications, including sorting algorithms, data analysis, finding extrema in mathematical functions, and making decisions based on numerical data.

When we compare two 2-digit numbers, the 2-digit number with a bigger digit at the tens place is bigger than the other 2-digit numbers. If the digit at the tens places is same, then the number with a bigger digit at the ones place is bigger.

A number with a bigger digit in the tens place is bigger. 6 is bigger than 4, so 65 is bigger than 48.

A number with a bigger digit in the tens place is bigger. 7 is bigger than 5, so 78 is bigger than 52.

A number with a bigger digit in the tens place is bigger. 6 is bigger than 2, so 63 is bigger than 29.

A number with a bigger digit in the tens place is bigger. 9 is bigger than 8, so 99 is bigger than 81.