Compare Two Decimals to Hundredths

Have you ever seen a price tag that says $3.49 or a stopwatch that reads 12.75 seconds? Those little dots and extra digits are called decimals. People did not always write numbers this way. For a very long time, fractions were the only tool people had for showing parts of a whole. Let's take a quick trip through history to see how decimals were invented!

So why do we need to compare decimals? Imagine you are at a store and one toy costs $4.59 and another costs $4.52. Which one is cheaper? To answer that, you need to know how to look at two decimals and decide which is greater, which is less, or if they are equal. That is exactly what this lesson is all about!

Before we start comparing, let's review four important ideas that will help everything make sense.

One of the best ways to understand decimals is to draw them. A hundredths grid is a square split into 100 tiny boxes. Each small box stands for one hundredth (0.01). When you shade boxes, you can see how big a decimal really is. Let's look at two decimals side by side: 0.47 and 0.63.

When you look at the picture, it is easy to see that 0.63 fills up more of its grid than 0.47. More shaded squares means a bigger number. That is what comparing decimals is all about: figuring out which amount is greater. You don't always need to draw a grid, but it's a great tool when you are first learning!

Here is a simple method you can use every time you compare two decimals. Follow these three steps, and you will always get the right answer.

Step 1: Line Up the Decimal Points

Write the two numbers on top of each other so that the decimal points are in a straight line. If one number has fewer digits after the decimal point, add a zero at the end to make them the same length. Remember, adding a zero after the last decimal digit does not change the number's value. For example, 0.3 becomes 0.30.

Step 2: Compare Digit by Digit, Left to Right

Start at the ones place (the digit before the decimal point). If those digits are the same, move to the tenths place. If those are the same too, move to the hundredths place. As soon as you find a place where the digits are different, the number with the bigger digit in that place is the greater number.

Step 3: Write the Symbol

Use > (greater than), < (less than), or = (equal to) between the two decimals. A fun trick: the open side of the > or < symbol always points toward the bigger number, like a little mouth that wants to eat the larger amount!

A number line is a straight line with numbers placed in order from least to greatest. When you place decimals on a number line, the one farther to the right is always greater. Let's look at where some decimals land between 0 and 1.

Look at the number line above. The decimal 0.25 is closest to zero, so it is the smallest. The decimal 0.78 is farthest to the right, so it is the greatest. We can write: 0.25 < 0.40 < 0.52 < 0.78. Any time you place two decimals on a number line, the one on the right is always the bigger one.

Here's a handy shortcut: you can think of each decimal to the hundredths as a whole number of hundredths. The decimal 0.25 means 25 hundredths, and 0.78 means 78 hundredths. Since 25 < 78, you know right away that 0.25 < 0.78. This trick works great because comparing whole numbers is something you already know how to do!

Let's walk through a full problem together. We will compare 0.8 and 0.76.

Did you notice something? Even though 0.76 has more digits, it is actually the smaller number! This is a very common trick question. The number of digits does not tell you which decimal is bigger — place value is what matters.

When students first learn to compare decimals, there are a few mistakes that pop up a lot. Let's go over them so you can avoid them.

Comparing decimals to the hundredths is a skill you will use over and over again. Here's a peek at what comes next as you move through math.

In 5th grade, you will compare decimals that go even further — to the thousandths place. But the method is exactly the same! You still line up the decimal points, compare left to right, and use the same symbols. So the work you are doing right now is building a strong foundation for everything ahead.

You will also start to see that decimals, fractions, and percentages are just three different ways to write the same number. For example, the decimal 0.50 is the same as the fraction ½ and the percentage 50%. Cool, right?

Time to try it yourself! Work through each problem, then click "Show Answer" to check your work. Don't peek too early — the best learning happens when you try first!