Whole Numbers and Integers: Background You’ll Need 2
Determine which number is larger
In the world of mathematics, understanding how to compare whole numbers and determine their relative magnitudes is a fundamental skill. Whether you’re analyzing data, solving problems, or making informed decisions, the ability to accurately compare numbers is essential.
Order and Place Value Matters
When determining which number is larger, we need to understand the basics of number order and place value. Each number has place values that start from the right and move left. The more place values a number has, the larger it is.
How we count also has a play into this. When we start at [latex]0[/latex] and then move on to [latex]9[/latex], each number along the way is larger than the previous. So, [latex]0[/latex] is smaller than [latex]1[/latex], [latex]1[/latex] is smaller than [latex]2[/latex], etc.
Once we get to the tens place, we start the cycle over again. So, [latex]10[/latex] is smaller than [latex]11[/latex], [latex]11[/latex] is smaller than [latex]12[/latex], etc.
This continues forever and ever again to infinity.
Let’s look at an example to determine which number is larger.
Between the following two numbers, which one is larger?
[latex]53[/latex] or [latex]46[/latex]
We first notice that both numbers have two place values, meaning they both between [latex]10[/latex] and [latex]99[/latex]. We then look at the number all the way to the left for each one.
[latex]53[/latex] starts with a [latex]5[/latex] in the tens place.
[latex]46[/latex] starts with a [latex]4[/latex] in the tens place.
Since [latex]5[/latex] is larger than [latex]4[/latex], we can safely say that [latex]53[/latex] is the larger number and we don’t have to look any further.
Note: If we only looked at the ones place, we would see that [latex]53[/latex] ends with a [latex]3[/latex] and [latex]46[/latex] ends with a [latex]6[/latex]. [latex]6[/latex] is the larger value, but since we have a difference in the tens place, that is the deciding factor to which number is larger.
Now let’s try another example of which number is larger.
Between the following two numbers, which one is larger?
[latex]314[/latex] or [latex]329[/latex]
We first notice that both numbers have three place values, meaning they both between [latex]100[/latex] and [latex]999[/latex].
We then look at the number all the way to the left for each one.
[latex]314[/latex] starts with a [latex]3[/latex] in the hundreds place.
[latex]329[/latex] starts with a [latex]3[/latex] in the hundreds place.
Since these numbers both start with a [latex]3[/latex], we need to look at the next place vale. The tens place.
[latex]314[/latex] has a [latex]1[/latex] in the tens place.
[latex]329[/latex] has a [latex]2[/latex] in the tens place.
Since [latex]2[/latex] is larger than [latex]3[/latex], we can safely say now that [latex]329[/latex] is the larger number and we don’t have to look any further.