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### Course: Arithmetic>Unit 16

Lesson 3: Multiplying decimals

# Developing strategies for multiplying 2-digit decimals

Learn to multiply decimals by treating them as fractions. Practice converting decimals to fractions and then multiplying like usual. Then convert the fractions back to decimals to solve!

## Want to join the conversation?

• Is there an easier way to do this? I mean, what if you don't have a piece of paper and can't write that well on the computer? Is there some way you could do this in your head?
(22 votes)
• you can do this in your head!
(4 votes)
• How do you multiply a big whole number, like 217 with a long decimal like 19.45? I've looked for a while for a video on that, but can't find one. I'm guessing you just do what Sal said but don't count any places over the decimal. But I'm not sure so please respond.
(8 votes)
• One way we can multiply those numbers or digits is area model or standard
(9 votes)
• Can't you just use the standard algorithm for this or just multiply them without decimals and add the m later on.
(9 votes)
• Yes, you could, but the will lower you concept of you understanding how multiplying with decimals work. Try learning the right way first then using any tricks.
(6 votes)
• What is 0.24 x 0.0009897 ? How do U solve that?
(4 votes)
• You multiply 24 times 9897 and then you move the decimal 9 places to the left.
(10 votes)
• how do you do it when the first digit in the number is 0?
(6 votes)
• can you do a problem like 0.08 times 0.38
(7 votes)
• Yes, you can.
EX:
0.08
x 0.38
------ You would do the regular standard algorithm then count how many digits
that are to the right to the right of the decimal points. That is how many digits are after you decimal point. So you count from the right of your answer the amount of digits that are after the decimal point and that is where you put your decimal point.
(0 votes)
• Example: 3.14 x 2.5. SO first thing to do is to line them up like regular multiplacation.

Do all the math, and dont place the decimal point yet. So you get the answer of 7850. So, in the equation, you looke at the factors. 3.14 has 2 decimal places, and 2.5 has 1. So 2+1=3, so start at the farthest to the right decimal value, and do three jumps between the numbers, or just go 3 numbers in from the smallest decimal value. If you did everything correctly, the answer is 7.850, or 7.85.
(3 votes)
• Learn to multiply decimals by treating them as fractions. Practice converting decimals to fractions and then multiplying like usual. Then convert the fractions back to decimals to solve!
(2 votes)
• what do u mean by 3 1/10?
(1 vote)
• three is the whole number and 1/10 is the fraction.
its a mixed number.
(2 votes)
• why does counting the number of digits after the decimal work?
(0 votes)
• Decimals are fractions just wrote in a different format, so if you think in terms of fractions and multiply 1/10 by 1/10 (0.1 * 0.1) the answer will result in one hundredth 1/100 (0.01). Anytime we multiply two fractions we multiply the denominators as well, so the pattern of counting how many digits are after the decimal point is knowing what the denominators are and what their product will be.
(4 votes)

## Video transcript

- [Instructor] Let's say I want to multiply 3.1 or 3 1/10 times times 2.4 which could also be described as 2 4/10ths so pause the video if you can do this and once again, I'll give you a hint. See if you can express these as fractions. So there's a couple ways you can express it as a fraction. You can express this as 3 1/10th times 2 4/10ths two, let's get the same color, 2 4/10ths. Now whenever you're multi these are mixed numbers right over here and mixed numbers are not the super straightforward to multiply, it's easier if they were written as what's often known as improper fractions but essentially not as mixed numbers. So three is the same thing as 30/10ths. So 30/10ths plus 1/10th, this is 31 10ths times two is the same thing as 20/10ths. So 20/10ths plus four is 24/10ths. 24 over 10. And hopefully this makes sense too that 3.1 this three right over here, this is 30/10ths or I can write, let me write 30/10ths and that this is 1/10th. So this total is going to be 31/10ths. Likewise, this two is 20/10ths plus 4/10th because it's 24/10ths. And now we can multiply. So this is going to give us our denominator's pretty straightforward. 10 times 10 is 100 and then 31 times 24, we can multiply in the traditional way that we're used to multiplying two digit numbers. 31 times 24 is going to be equal to four times one is four, four times three is 12, now we're gonna be multiplying in the tenths place. We're going to put a zero here. So two times one is two. We're really saying 20 times one is 20. But you get the idea. Two times one is two. Two times three is six. Really 600, because it's 20 times 30. But I'm just following the standard multi the method for multiplication then you add these. And you're gonna get four four seven. So when you multiply these two things together, in the numerator, you get 744 100ths. Which can also be expressed as this is the same thing as 700ths or 700 100ths I should say, plus 44/100ths and 700/100ths, that's just going to be equal to seven. So this is seven plus 44/100ths which we could write as .44 that's our seven and 44/100ths. And we would be done. And you might already be seeing a pattern. If you just took 31 and multiplied it by 24, you get 744. And notice, I have one and two digits behind the decimal point. Notice I have one and two digits behind the decimal point. And so think about whether that always works. Think about and why that might work. If you just multiply the numbers as if they didn't have decimals, so you would've gotten 744 and you say, I got two numbers behind the decimal, so my product is going to have two numbers behind the decimal, why does that work? Or does it always work? And how does it relate to what we did here which is converting these things to improper fractions and then multiplying it that way?