We use numbers and know many things about them. Numbers help us
count concrete objects. They help us to say which collection of objects
is bigger and arrange them in order.
Place Value
Place value is a fundamental concept in mathematics that determines the value of a digit based on its position within a number. We use a base-10 number system, each position represents a power of 10. For example, in the number 9562, the digit ‘2’ is in the ones place, ‘6’ is in the tens place, and ‘5’ is in the hundreds place. and ‘9’ is in the thousands place. So, the place value of ‘2’ is 2, the place value of ‘6’ is 60, the place value of ‘5’ is 500 and the place value of ‘9’ is 9000. This system allows us to express large numbers efficiently.
Comparing Numbers
We compare two numbers and denote comparison marks in between:
- Greater than denotes by >
- Less than denotes by <
- Equal denotes by =
Comparing numbers involves looking at the place value of each digit from left to right. Here’s a step-by-step guide:
First, count the number of digits and the number which has more digits is greater. If the number of digits are equal then we start comparing the first digit from the left. The number with the greater digit is the larger number. If these digits are equal, move on to next place (the second digit from the left) and compare them in the same way. Keep moving to the right, comparing digits in the hundreds, tens, and ones places until you find a difference.
If you find a difference in any place value, you can determine which number is greater based on that difference.
Equal Numbers: If all corresponding digits are equal, the two numbers are equal.
For Example:
- Compare 5689 and 12569
- First, count the number of digits (5689 has 4 digits & 12569 has 5 digits) and the number which has more digits is greater, hence 5689 < 12569
- Compare 5214 and 2986
- First, count the number of digits (both have 4 digits), If the number of digits are equal then we start comparing the first digit from the left (5 and 2). We find 5>2, hence 5214 > 2986
- Compare 98216 and 98215
- First, count the number of digits (both have 5 digits), If the number of digits are equal then we start comparing the first digit from the left (9 = 9). If these digits are equal, move on to next place (the second digit from the left (8 = 8)) and compare them in the same way. Keep moving to the right, comparing digits in the hundreds, tens, and ones places until you find a difference (6 > 5). Hence 98216 > 98215
- Compare 6523 and 6523
- After follow each step mentioned above, we do not find any difference, so 6523 = 6523