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What is a decimal?

Basic Decimals

What is a decimal?

A decimal is a number that has a decimal point followed by digits that show a value smaller than one.

Think of the parts of a decimal like money:

The 12 represents whole dollars and is separated from the coins with the decimal point. The 85 cents are not enough to complete one whole dollar so they are on the other side.

In this way, think of a decimal point as a fence that separates the whole dollars, from the parts of dollars, aka, cents.

Try comparing decimals with our calculator below ⬇️.

Decimal Comparison Calculator

Decimal A:

Decimal B:

One of our decimals is negative and the other isn't! So let's pull out our number line:

See how positive decimals are always bigger than negative decimals (just like integers)? So, any positive decimal is always going to be bigger than any negative decimal.

One of our decimals is 0, so let's take a look at our number line:

Remember that positive numbers are greater than zero, and negative numbers are less than zero. Since is negative, it must be the smaller of the two decimals!

Step 1: Line Up Decimal Points

The first step to comparing decimals is to line up the decimal points. Drag the bottom decimal to line them up!

Perfect! Now that the decimal places are aligned, we can start comparing the digits!

Step 2: Check the Lengths

Next, we need to make sure both decimals are the same length.

If our decimals are the same length, we don't need to do anything. But if they're not, we can add zeros to the end or beginning of the decimals to match them up.

Step 3: Compare Digits

Next, we need to compare our digits, starting from the left.

If the numbers are the same, we move right one place value and compare. Keep going until the digits are different.

Try it out - select the first place value where the digits are different.

Not quite... start from the left, and pick the FIRST place that has different digits.

Step 4: Final Comparison

Exactly! Now, since both our numbers are positive, the decimal that has the larger digit from above will be the larger decimal! Which decimal is larger?

Not quite... which decimal had the larger digit in the place you selected above?

You rock! That's right! 🎉 is bigger than .

basketball

To learn more about when we use decimals, what place values are, and which zeros matter in a decimal number, click below!

When do we use decimals?

Whenever we're dealing with numbers that aren't whole numbers, decimals can help us out. If we zoom in on a number line, we see that decimals lie in between whole numbers.

-4

-3

-2

-1

0

1

2

3

4

And notice that just like negative whole numbers, negative decimals get SMALLER as the number itself gets BIGGER.

Fractions or Decimals or Both?

The idea of “parts of the whole” may sound a bit familiar. Fractions and decimals both represent parts of the whole. The difference between the two is the way they are presented.

A fraction has a division bar, with a number above (numerator) and a number below (denominator).

Meanwhile, a decimal has a decimal point with the whole number value to the left and the “part of the whole” to the right. If some of this fraction talk is confusing or not ringing any bells, let’s review here!

What is a place value?

A place value tells us how big or small a digit is based on its position relative to the decimal point. Because they tell us the size of each digit, they are important when we start comparing two decimals together.

Think of a place value as a compartment in a cash register. The compartment that each piece of money is in tells us how valuable the money is (aka the bills in the $100 section are more valuable than the bills in the $1 section).

Some Common Place Values

Place values get their names from the value of the number that is created with a “1” in that position, and "0"s in every other position.

NumberExpress in wordsPlace value of the "1"
1,000one thousandthousands
100one hundredhundreds
10tentens
1oneones
0.1one tenthtenths
0.01one hundredthhundredths
0.001one thousandththousandths

Let’s do a little practice! Match each decimal with the name of the place value that is highlighted:

Let's put it all together!

Cashiers have to deal with place values all the time. When calculating how much change to give a customer, we want to go from left to right in the number, and try to use as few bills and coins as possible.

541.73
Cash Register With Clamps
hundredStacks
tenStacks
oneStacks
dimes
pennies
0
0
0
0
0

Total: $0.00


Which zeros matter?

Just like with whole numbers, some zeros are important and others are not.

Let’s take the number 1,000. Which of the following is not equal to 1,000?

That’s right! If we add a zero in the middle of 1,000, we get 10,000 which is not the same as 1,000.

In the part before the decimal point, we can add or remove zeros at the front, but not in the middle or end.

For digits after the decimal point, the reverse is true. Let’s take 0.1 or one tenth. Which of the following is not equal to 0.1?

That’s right! In the part after the decimal point, we can add or remove zeros at the end only, not in the front or middle.

Does the zero matter?

Here's a chart to help you remember!

flow chart

Quick Practice 1 / 3

72.5
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