Introduction to multiplying decimals | Decimals | Pre-Algebra | Khan Academy

Summary

The video script offers a detailed explanation of multiplying 9 by 0.6. It begins by encouraging viewers to calculate the result themselves, then provides a hint that 0.6 is equivalent to 6 divided by 10. The script proceeds to demonstrate the multiplication by first calculating 9 times 6, yielding 54, and then dividing by 10 to account for the decimal, resulting in 5.4. The presenter highlights the pattern of decimal places and invites viewers to consider whether the number of digits after the decimal in the factors determines the number of digits after the decimal in the product.

Takeaways

• 🔢 The script begins with a multiplication problem: 9 times 0.6.
• 📝 It suggests rewriting 0.6 as 6 divided by 10 to simplify the calculation.
• 📚 The concept of moving the decimal place is explained as dividing by 10.
• 🤔 The viewer is encouraged to pause and attempt the problem independently.
• 📉 The hint provided is that 6.0 divided by 10 equals 0.6, moving the decimal one place to the left.
• 📈 The multiplication strategy involves first calculating 9 times 6, then dividing by 10.
• 🎯 The result of 9 times 6 is 54, which is then divided by 10 to get the final answer.
• 📌 The division by 10 is illustrated by adding a decimal and moving it one place to the left.
• 📉 The final answer for 9 times 0.6 is given as 5.4.
• 🧩 The script highlights a pattern where the number of digits to the right of the decimal in the factors determines the number of digits to the right of the decimal in the product.
• 💭 It invites the viewer to consider whether this pattern is a general principle for multiplication involving decimals.

Q & A

What is the initial multiplication problem presented in the script?

The initial multiplication problem presented in the script is to calculate 9 times 0.6.

What is the hint given to help understand the multiplication of 9 by 0.6?

The hint given is that 0.6 is equivalent to 6 divided by 10, which can be visualized by moving the decimal point one place to the left.

Why is it suggested to pause the video and try to figure out the multiplication on one's own?

It is suggested to pause the video to encourage active learning and personal problem-solving, allowing viewers to engage with the material more deeply.

What is the alternative method to calculate 9 times 0.6 presented in the script?

The alternative method is to first calculate 9 times 6, which equals 54, and then divide the result by 10 to account for the decimal in 0.6.

How does dividing by 10 affect the decimal place in a number?

Dividing by 10 shifts the decimal place one position to the left, effectively reducing the number by a factor of 10.

What is the result of the multiplication 9 times 6?

The result of the multiplication 9 times 6 is 54.

What is the final result of the multiplication 9 times 0.6 after dividing by 10?

The final result of the multiplication 9 times 0.6, after dividing by 10, is 5.4.

What pattern is observed between the numbers 54 and 5.4 in the context of this multiplication?

The pattern observed is that when multiplying by a decimal, the number of digits to the right of the decimal in the multiplier corresponds to the number of digits to the right of the decimal in the product after division.

What does the script suggest as a general principle for multiplying whole numbers by decimals?

The script suggests that you can multiply the whole numbers first, ignoring the decimal, and then adjust the product by dividing by 10 for each digit to the right of the decimal in the original multiplier.

How does the script use the concept of decimal notation to explain the multiplication process?

The script uses the concept of decimal notation to explain that each place value to the right of the decimal represents 1/10 of the place to its left, which is why dividing by 10 moves the decimal one place to the left.

What is the significance of the pattern discussed in the script for understanding multiplication with decimals?

The significance of the pattern is that it provides a visual and conceptual framework for understanding how the position of the decimal point affects the product in multiplication, which can be a helpful tool for problem-solving with decimals.

Outlines

00:00

🔢 Multiplication of 9 by 0.6

The paragraph introduces a multiplication problem involving the number 9 and the decimal 0.6. It encourages the viewer to pause and attempt the calculation independently, hinting that 0.6 can be understood as 6 divided by 10. The explanation proceeds by demonstrating the multiplication of 9 by 6 and then dividing the result by 10 to account for the decimal, resulting in 54 divided by 10, which equals 5.4. The paragraph concludes by highlighting a pattern observed in the multiplication involving decimals, suggesting that the number of digits to the right of the decimal in the factors may influence the product's decimal placement.

Keywords

💡multiply

To multiply is to find the product of two or more numbers, which means adding one of the numbers to itself the other number of times. In the video, the term is used to discuss the process of finding the result of 9 times 0.6, which is the main mathematical operation being explained.

💡decimal

A decimal is a number that represents a fraction with a denominator of 10 or a multiple of 10. It is used to express parts of a whole. In the script, the decimal 0.6 is explained as 6 divided by 10, which helps to clarify the concept of moving the decimal point in division.

💡division

Division is the mathematical operation of dividing a number into equal parts. In the video, division by 10 is used to convert the fraction 6/10 into the decimal 0.6, and later to find the result of 9 times 0.6 by dividing 54 by 10.

💡decimal place

The decimal place refers to the position of digits after the decimal point in a number. The script explains that moving the decimal place to the left is equivalent to dividing by 10, which is crucial for understanding the multiplication of 9 by 0.6.

💡hint

A hint is a suggestion or clue given to help someone solve a problem or understand a concept. The video provides a hint that 0.6 is the same as 6 divided by 10, which is essential for grasping the subsequent explanation.

💡pause

To pause means to temporarily stop or interrupt an activity. In the context of the video, the speaker encourages viewers to pause the video to try solving the problem independently, which is a common educational technique to engage the audience.

💡calculate

To calculate is to compute or determine a result using mathematical methods. The video script involves calculating 9 times 0.6, which is the central problem that the video aims to solve.

💡equivalent

Equivalent means being equal in value, function, or meaning. The script uses the term to explain that 6 divided by 10 is equivalent to the decimal 0.6, which is a fundamental concept in the explanation.

💡product

The product is the result of multiplication. In the video, the product of 9 times 6 is calculated as 54, and then the concept is applied to find the product of 9 times 0.6.

💡pattern

A pattern is a regularity or sequence of events or phenomena. The video script suggests a pattern where the number of digits to the right of the decimal in the factors determines the number of digits to the right of the decimal in the product.

💡general principle

A general principle is a fundamental truth or proposition that serves as the foundation for a system of belief or behavior. The video ends by prompting the viewer to consider whether the observed pattern regarding decimal places is a general principle that can be applied to other multiplication problems involving decimals.

Highlights

The task is to multiply 9 by 0.6.

0.6 can be written as 6 divided by 10.

Dividing by 10 moves the decimal place one position to the left.

Calculating 9 times 6 gives 54.

Dividing 54 by 10 results in 5.4.

Multiplying 9 by 0.6 is equivalent to multiplying 9 by 6 and then dividing by 10.

Decimal notation and its implications are discussed.

Each decimal place represents 10 times more or 1/10 of the place to its right.

Multiplying 9 by 6 and then dividing by 10 is a method to handle decimal multiplication.

The result of 9 times 0.6 is 5.4.

The pattern between 9 times 6 and 9 times 0.6 is highlighted.

The number of digits to the right of the decimal in the multiplier affects the result.

A general principle is suggested regarding the number of decimal places in the product.

The video encourages viewers to pause and try the calculation themselves.

The explanation uses a step-by-step approach to simplify the concept.

The video provides a clear demonstration of how to handle decimal multiplication.

Transcripts

Let's see if we can multiply 9 times 0.6.

Or another way to write it, we want to calculate 9 times 0.6.

I'll write it like this-- 0.6.

We want to figure out what this is equal to.

And I encourage you to pause the video

and try to figure it out on your own.

And I'll give you a little bit of a hint.

0.6 is the same thing as 6 divided by 10.

We know that if we start with 6, which we could write as 6.0,

and if you were to divide it by 10, dividing by 10

is equivalent to moving the decimal place one

place to the left.

So 6 divided by 10 is 0.6.

We are moving the decimal one place to the left.

So I'm assuming you given a go at it.

But what I'm going to do is use this

that we already know to rewrite what we're trying to multiply.

So 9 times 0.6 is the same thing is 9 times--

0.6 is 6 divided by 10.

And this expression right over here,

we could either do the 6 divided by 10 first, in which case

we would get 0.6, and this would turn into this problem.

Or we could do the 9 times 6 first.

And so let's do 9 times 6, which we know how to calculate,

and then divide by 10, which we also know how to do.

That.

all about just moving the decimal place.

So we could write 9 times 6.

9 times 6, we already know, is 54.

I'll do that in orange-- is going to be 54.

So this right over here is 54.

And now to get to this expression,

we have to divide by 10.

We have to divide by 10.

And what happens when we divide something by 10?

And we've seen this in previous videos, why this is the case.

This is all about what decimal notation means.

Each place represents 10 times as much as the place

to its right, or each place represents 1/10 of the place

to the left.

So 54 divided by 10, this is going

to be-- you could start with 54.

And I'll put a 0 here after the decimal.

And when you divide by 10, that's

equivalent of shifting the decimal one to the left.

This is going to be equal to 5.4.

And that should make sense to you.

5 times 10 is 50.

0.4 times 10 is 4.

So it makes sense that 54 divided by 10--

I shouldn't say equal.

I'd write 54 divided by 10 is equal to 5.4.

So this right over here is equal to 5.4,

and that's what this is.

This is equal to 5.4.

Notice, 9 times 6 is 54.

9 times 0.6 is 5.4.

Now you might see a little pattern here.

Between these two numbers, I had exactly one number

to the right of the decimal.

When I take its product, let's say I ignored the decimal.

I just said 9 times 6, I would've gotten 54.

But then I have to divide by 10 in order

to take account of the decimal, take

account of the fact this wasn't a 6.

This was a 6/10.

And so I have one number to the right of the decimal here.

And I want to you to think about that

whether that's a general principle.

Can we just count the total numbers of digits

to the right of the decimals and then

our product is going to have the same number of digits

to right of the decimal?

I'll let you to think about that.