Decimals

This course is a part of Arithmetic, a 6-course Topic series from Khan Academy.

In this topic, we will learn what a decimal is and how to show it visually and on a number line. We will also add, subtract, multiply, and divide with decimals.

This course contains 14 segments:

Intro to decimals

What are decimal numbers? How are they like fractions?

Decimal place value intro

Learn the basics of decimal place value.

Decimals on the number line

See how decimals can be placed on the number line, just like fractions and whole numbers can.

Rewriting decimals as fractions

Learn how to rewrite decimals as fractions.

Adding decimals

You get the general idea of decimals and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

Adding decimals: standard algorithm

Honestly, once you remember one very important rule, the rest of adding and subtracting decimals is a snap. That rule is to be sure and align your decimals first. In this tutorial, you'll get a chance to practice this with us and become fluent adding decimals. We'll tackle subtracting decimals in the next tutorial.

Subtracting decimals

Anything you can do with whole numbers, you can do with decimals. Subtraction is no exception. In this tutorial, you'll get some good practice subtracting decimals up the hundredths place.

Subtracting decimals: standard algorithm

Just like with adding decimals, the key to subtracting decimals is aligning the decimal points. Let's practice!

Adding and subtracting decimals word problems

In this tutorial, we practice solving word problems by adding and subtracting decimal numbers.

Multiplying decimals

The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.).

Multiplying decimals: standard algorithm

You've already multiplied decimals in the 5th grade. We'll show you some ways to handle slightly more complicated problems. Now you'll become super good at it with a bit more practice! Common Core Standard: 6.NS.B.3

Dividing decimals

In this tutorial, we'll extend our division skills to include decimals! We get into some pretty fun stuff here including dividing decimals by whole numbers, and dividing whole numbers by decimals. Finally...dividing decimals by decimals. Common Core Standard 5.NBT.B.7

Dividing decimals: standard algorithm

Learn long division with decimals. Solve problems like 30.24 divided by 0.42.

Significant figures

There is a strong temptation in life to appear precise, even when you are aren't accurate. If you precisely measure one dimension of a carpet to be 3.256 meters and eyeball the other dimensional to be "roughly 2 meters", can you really claim that the area is 6.512 square meters (3.256 x 2)? Isn't that a little misleading? This tutorial gets us thinking about this conundrum and gives us the best practices that scientists and engineers use to not mislead each other.