Decimals : Khan Academy on a Stick

Khan Academy on a Stick

Pre-algebra

Decimal place value
Decimal Place Value
Decimals: writing it out in words
By writing out a decimal in words, you're forced to really show your understanding of it. Give it a try!
Decimals: writing it out in words 2
Here's another example involving writing out a decimal in words. Great practice.
Decimals: expanding out place value
Let's expand a decimal out and really try to understand what it represents.
Decimals: writing it out as a number
Take your time and remember your order of operations as you translate this into a decimal number.
Decimals: comparing place values
We're having a blast with decimals! Check this one: we're comparing place values. This will blow your mind.
Decimals: choosing a number to represent place value
Let's decide the number of each place value to make the given decimal. We can do it together!

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 with decimals
We're doing more regrouping but this time using decimals. Just remember those place values!
Regrouping with decimals example 1
Similar to a problem we did earlier but with whole numbers, this time we're having to regroup with decimals and find the right answer. Take your time.
Regrouping decimals example 2
Great decimal regrouping exercise. Do this one with us and see how well you've mastered the regrouping decimal topic!

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 compare decimals on a number line, shall we?
Decimals and fractions on a number line
We're mixing it up by placing both fractions and decimals on the same number line. Great practice because you need to move effortlessly between the two.
Placing positive and negative decimals on a number line
These example exercises require us to interpret a number line in order to locate where our positive and negative decimals should be placed.

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 example 1
When comparing decimals it's easy to get confused by the number of digits to the right of decimal. Is it a tenth, hundredth, or thousandth? This video will help you a lot!
Comparing decimals example 2
We're using the less than (<) and greater than (>) symbols to compare decimals now. Cool!
Comparing decimals: difference in largest place value
Confused trying to determine which decimal is larger? Let's compare two decimals in this example. Remember that you're looking for the difference is the largest place value to find the larger decimal.
Comparing decimals: place value difference
It's not uncommon to be asked to compare two decimals and judge which one is larger. How do you do that? This video will gave you the confidence to answer that question.
Comparing decimals: ordering from least to greatest
This is a fun example where we reorder decimals from smallest to largest. You're looking for the place value that is the most signifiant, and then working backwards.
Comparing decimals: ordering from smallest to biggest
Let's move the decimals around and reorder them from least to greatest. Hint: look at one place value and then compare it to the decimals before moving on to the next place value.

Comparing decimals

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

Adding decimals: example 1
Line those decimals up first. Careful!
Adding decimals: example 2
Let's practice another adding decimal problem. We'll do it together.
Adding decimals: example 3
We're adding 3 decimal numbers together in this example. Give it a try!
Subtracting decimals: example 1
Subtracting decimals...up to the hundredths placement. Line up those decimals before you start.
Subtracting decimals example 1
Just like when add, be sure you align decimals before subtracting.
Adding decimals word problem
Here's a simple word problem asking us to put our adding decimals skill to work. We sound like a broken record, but be sure and ALIGN DECIMALS.
Adding and subtracting decimals word problem
Let's get fancy and practice adding and subtracting decimals in the same word problem.
Subtracting decimals (old)
Subtracting decimal numbers

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!

Introduction to multiplying decimals
Multiplying decimals can be confusing because there's always the question as to where the decimals goes in the answer. We're about to show you so you'll never have to question it again!
Multiplying decimals word problem
We're multiplying decimals again, but this time answering a common question: what's the cost of filling up the car tank?
Multiplying decimals: place value and reordering
We want you to develop an intuition about how to work with decimals. Understanding how you can rewrite decimals by considering the place value will help you multiply!
Multiplying decimals example
Multiplying decimals? Try multiplying without the decimals first, them add them back in. We'll show you.
Multiplying challenging decimals
Sometimes multiplying really small decimals (with all those zeros!) can be a little intimidating. Watch as we show you a handy trick to simplify these problems and solve them.

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 completely to get decimal answer
Sometimes, in order divide numbers completely you have to add a decimal and bring down places. Let's do it together, shall we?
Dividing completely to get decimal answer example 2
Sometimes the number that you're dividing by is smaller than the number that is being divided and won't go into it even once! What do you do? Watch.
Dividing a decimal by a whole number
You're doing great. Now we want to mix it up a little: divide a decimal by a whole number. Follow along.
Dividing a whole number by a decimal
When dividing a whole number by a decimal, you're going to need to change that decimal into a whole number. How? We'll show you.
Dividing by a multi-digit decimal
Let's do one more decimal division problem together but change it up. This is one with a decimal divisor and will require you to shift the decimal first.
Dividing decimals with hundredths example 3
The old saying is "practice makes perfect." Let's keep practicing dividing decimals and making our divisor a whole number.

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!!!!!

Fraction to decimal with rounding
Sometimes when you convert a fraction to a decimal you have to do some long division and rounding.
Fraction to decimal example
This is a great example of converting a fraction to a decimal. Use a scratch pad so you can follow along.
Converting fractions to decimals
How to express a fraction as a decimal
Fraction to decimal
Converting fractions to decimals sometimes requires us to brush up on our long division skills. We'll walk you through it.
Decimal to simplified fraction
Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you.
Converting decimals to fractions example 1
We're practicing how to convert a lonely decimal into a happy fraction.
Converting decimals to fractions example 2
Being a decimal is hard. Everyone picks on you. Not like those lucky fractions. Let's convert the decimal together.
Converting decimals to fractions example 3
Converting this decimal results in a fraction that needs to be simplified. Can you help us?
Converting decimals to fractions 2 (ex 1)
Converting decimals to fractions 2 (ex 2)

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?

The meaning of percent
Let's start by thinking about what percent really means. Once you understand this, other pieces will begin to fall into place.
The meaning of percent over 100
How does our meaning of percent (per "hundred") translate when we need to understand a percent OVER a hundred?
Converting percent to decimal and fraction
You'll find that be able to move easily between percentages, decimals, and fractions is HUGELY helpful. So let's practice!
Converting decimals to percents
Need to convert a decimal to a percent? Ok, we'll just use our fraction friends to get us there. Watch and be amazed.
Converting decimals to percents example 2
Understanding how to convert a decimal to a percent comes in really handy sometimes. Let's practice using this problem.
Converting percents to decimals
Remember that "per cent" means "per hundred." Knowing that, converting a percent to a decimal is done by dividing by a 100. We'll demonstrate.
Converting percents to decimals example 2
Practice another conversion problem, this time from percent to decimal. Arriving at the answer is as simple as dividing by 100!
Finding a percentage
Once again, fractions are our friends as we use them to find a percentage. You'll also see a couple of different ways to arrive at the answer.
Percent word problem
It's nice to practice conversion problems, but how about applying our new knowledge of percentages to a real life problem like recycling? Hint: don't forget your long division!
Identifying percent amount and base
Identifying Percent Amount and Base
Representing a number as a decimal, percent, and fraction 2
Representing a number as a decimal, percent, and fraction 2
Ordering numeric expressions
Ordering numbers expressed as decimals, fractions, and percentages
Percentage of a whole number
We hope you're beginning to see that there's more than one way to skin a cat. In other words, there are several different ways to solve problems involving percentages, decimals, and fractions. Watch as find the percentage of a whole number.
Basic example of rewriting a fraction as a decimal
Let's watch as Sal gives us a basic example of how to rewrite a fraction as a decimal. This will make a lot of sense!
Rewriting fraction as a decimal to the hundredths place
As our earlier example, the goal is to simply the fraction and then convert it--this time in terms of hundredths.

Intro to percentages

Growing by a percentage
In this example we grow a whole number by a percentage of itself. Growing by percentage is a common skill often used when figuring how much is owed or earned with interest.
Solving percent problems
We'll use algebra to solve this percent problem.
Percent word problem example 4
This word problem is expressed simply which can be confusing to some. Take your time and focus on the what is being asked for.
Percent word problem example 5
In this example, you working with us to find the number that is expressed as a given percentage.We'll create a simple algebraic equation to solve!

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.

Rounding decimals: to the nearest tenth
Rounding. Oh my....there will be so many times when rounding numbers (including decimals) will be a required skill. Let's get this down, shall we?

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
Introduction to significant figures
More on significant figures
Understanding the "rules of thumb" for significant figures
Addition and subtraction with significant figures
Addition and Subtraction with Significant Figures
Multiplying and dividing with significant figures
Multiplying and dividing with significant figures

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.

Multiplying a decimal by a power of 10
You will notice in this word problem that moving the decimal to the right the same number of times as the number of zeros you multiplying by gets you the answer you desire. Check this out!
Dividing a decimal by a power of 10
When we were multiplying, we moved the decimal to the right for each power of ten. Guess what? When dividing, we move the decimal to the left for each power of ten.
Dividing a decimal by a power of 10: shortcut
Holy cow! A shortcut? Yep. For each ten you multiply or divide by, just shift that decimal to the right or left. Watch this and be amazed.

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, subtracting numbers in different formats
In this example, we solve an addition problem with numbers in different formats: a percentage, decimal, and mixed number. First, we'll get them all in the same format...which makes it a while easier to solve!
Adding, subtracting fractions, decimals, percentages
What happens when we are asked to add or subtract fractions, decimals, and percentages? You'll see in this example that we first get them in the same format, and then add fractions.
Adding, subtracting fractions
Our focus here is on learning to multiply fractions. First we have to get the common denominator, then add positive and negative numbers.

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.