# Decimals

Contents

Understanding decimals conceptually, using operations with decimals, rounding and estimating with decimals, and converting decimals.

## Conceptualizing decimals and place notation

You've been using decimals all of your life. When you pay $0.75 at a vending machine, 0.75 is a decimal. When you see the ratings of gymnastics judges at the Olympics ("9.5, 9.4, 7.5 (booooo)"), those are decimals. This tutorial will help you understand this powerful tool all the better. Before you know it, you'll be representing numbers that are in-between whole numbers all the time!

## Regrouping decimals

Let's explore how we can regroup and redistribute value among the various place values in a decimal number.

## Decimals on a number line

Let's think about where decimals are on a number line. It will help us understand what decimals represent in general!

## Comparing decimals

Let's test our understanding of decimals by comparing them to one another!

## Adding and subtracting decimals

You get the general idea of decimal is 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!

## 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.).

## Dividing decimals

You can add, subtract and multiply decimals. You know you'd feel a bit empty if you couldn't divide them as well. But something more powerful is going to happen. If you are like us, you never quite liked those pesky remainders when dividing whole numbers. Well, those pesky remainders better watch out because they are going to be divided too!!!! Ah ha ha ha ha!!!!!

## Converting between fractions and decimals

Both fractions and decimals are desperate to capture that little part of our heart that desires to express non-whole numbers. But must we commit? Can't we have business in the front and party in the back (younger people should look up the word "mullet" to see a hair-style worth considering for your next trip to the barber)? Can't it look like a pump, but feel like a sneaker? Well, if 18-wheelers can turn into self-righteous robots, then why can't decimals and fractions turn into each other?

## Intro to percentages

At least 50% of the math that you end up doing in your real life will involve percentages. We're not really sure about that figure, but it sounds authoritative. Anyway, unless you've watched this tutorial, you're really in no position to argue otherwise.
As you'll see "percent" literally means "per cent" or "per hundred". It's a pseudo-decimally thing that our society likes to use even though decimals or fractions alone would have done the trick. Either way, we're 100% sure you'll find this useful.

## Percent word problems

Whether you're calculating a tip at your favorite restaurant or figuring out how many decades you'll be paying your student debt because of the interest, percents will show up again and again and again in your life. This tutorial will expose you to some of these problems before they show up in your actual life so you can handle them with ease (kind of like a vaccine for the brain). Enjoy.

## Estimating and rounding with decimals

Laziness is usually considered a bad thing. But sometimes, it is useful to be lazy in a smart way. Why do a big, hairy calculation if you just need a rough estimate? Why keep track of 2.345609 when you only need 2.35?
This tutorial will get you comfortable with sometimes being a little rough with numbers. By being able to round and estimate them, it'll only add one more tool to your toolkit.

## 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.

## Moving the decimal to multiply and divide by 10

In our decimal number system, as we move places to the left, the place values increase by a factor of 10 (likewise, they decrease by a factor of 10 as we move rightward). This idea gets direct application when we multiply or divide a decimal number by 10 because it has the effect of shifting every place value one to the right or left (sometime seen as moving the decimal point).

## Adding and subtracting decimals, percentages, and fractions

If you think you know how to convert between decimals, fractions and percentages and are familiar with negative numbers, this tutorial is a good place to test all of those skills at the same time.