Video: Multiplying Decimals by Integers

Calculate 0.0378 × 34.


Video Transcript

Calculate 0.0378 multiplied by 34.

In this calculation, we’re asked to multiply by a two-digit number, 34. But what makes this calculation one that we need to think about a little bit more carefully is that the number that we’re multiplying by 34 is a decimal number, 0.0378. How could we multiply a decimal by a two-digit number? It’d be much easier if we are multiplying two whole numbers together. Well, one way we can find the answer is to write out the digits from 0.0378 without the decimal point.

Now, those two zeros at the start don’t make any sense without a decimal point, so we can actually get rid of those. 378. And what we can do is multiply 378 by 34 and then, at the end, we can put the decimal point back into our answer to show what the product of the two numbers in our calculation really should be. So, to begin with, let’s multiply 378 by 34. We can start by multiplying the digits in 378 by the four digit in 34. In other words, we’re going to find the answer to 378 multiplied by four.

A quick way to multiply by four is to double and then double again. Eight doubled is 16. And then, 16 doubled is 32. So, we know eight times four is 32. To work out seven multiplied by four, we can double then double again. Seven doubled is 14. And 14 doubled is 28. And we’ve exchanged three underneath, so if we add that to 28, we then have 31.

Now, even though we may know what three times four is, let’s use the double-double method just to finish off. Three doubled is six, and six doubled is 12. We’ve got three hundreds underneath that we need to add to our 12 hundreds to give 15 hundreds. 378 multiplied by four is 1512. Now, we need to multiply 378 by the three digit in 34.

Now, of course, this stands for three tens or 30. We’re finding out the answer for 378 multiplied by 30. It would be a lot easier if we were just multiplying by three. We know that 30 is the same as 10 lots of three. So, we can write a zero as a place holder in the ones place, and this shifts all our digits one place to the left. So, it’s the same as multiplying by 10. And now, we can just multiply by three. What are eight threes or three eights? Let’s count in eight three times. Eight, 16, 24. Eight times three is 24.

Onto the tens digit, what are seven threes or three sevens? Let’s count in seven three times. Seven, 14, 21. And we’ve got two underneath that we’ve exchanged that takes us to 23. And finally, three times three. Three, six, nine plus the two that we’ve exchanged equals 11. 378 multiplied by 30 equals 11340.

Now, just like any other long multiplication, we need to add each column from right to left to find the overall total. Two ones plus zero ones equals two ones. One ten plus four tens equals five tens. Five hundreds plus three hundreds gives us eight hundreds. One thousand plus another one thousand equals two thousands. And finally, we’ve got one lot of 10000 in the ten thousands place.

And so, we’ve calculated the answer to 378 multiplied by 34. And the answer we found was 12852. But of course, this isn’t the question that we’ve been asked. We’ve been asked to calculate 0.0378 multiplied by 34. Now, we can go back to our original calculation and turn it back into a decimal. So, we’re going to write 0.0 at the start. And now it’s a 0.0378.

Now, all we have to do is work our way down the whole calculation and put the decimal point where it belongs, here. So, 0.0378 multiplied by four is 0.1512. Let’s keep going. We’ll put it here. So, 0.0378 multiplied by 30 is 1.1340. And then most importantly, we can put it into our answer here. To find the answer, we turn the decimal into an integer and then back again. 0.0378 multiplied by 34 equals 1.2852.

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