When multiplying decimals, instead of lining up the decimal point, we line up the last digits on the right.

So, if we were multiplying 4.23 times 9.075, we want to line up our last digits.

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The transcript is for your convenience.

So, 3 is the last digit in 4.23, and 5 is the last digit in 9.075. There’s my 7, and my 0, my decimal, and 9.

Now, we multiply just like we multiply whole numbers. So, starting with 5, 5 times 3 is 15, carry the 1. 5 times 2 is 10, plus 1 is 11, carry the 1. 5 times 4 is 20, plus 1 is 21, and then I’ll get rid of these for our next number.

Now that we’re multiplying times the 7, we need a 0 placeholder. 7 times 3 is 21, write your 1, carry your 2. 7 times 2 is 14, plus 2 is 16, write your 6, carry your 1. 7 times 4 is 28, plus 1 is 29. Get rid of those.

Then, we need two zeroes for placeholders, and when we multiply times 0, 0 times 3 is 0. 0 times 2 is 0, and 0 times 4 is 0, we just get a line of zeroes.

So, moving on to our last digit, now we need 3 zero placeholders before we multiply times 9. 9 times 3 is 27, write the 7, carry the 2. 9 times 2 is 18, plus 2 is 20, write the 0, carry the 2. 9 times 4 is 36, plus 2 is 38.

Then just like we would with any other whole numbers, we’re going to add our results together.

5 plus all these zeroes gives us 5. 1 plus 1 is 2. 1 plus 6 is 7. 2 plus 9 is 11, plus 7 is 18, write our 8, carry our 1. 1 plus 2 is 3. And then we have 8, and our 3.

To determine where the decimal point goes when you’ve multiplied your decimals together, we’re going to take how many places, how many numbers that were behind our decimal in our first number, and how many numbers there were behind our decimal in our second number, and add those together.

So, since we had two numbers behind the decimal here, and three numbers behind the decimal here, then our result will have five numbers behind the decimal. 2 plus 3 is 5. 1, 2, 3, 4, 5.

So, this is the result of multiplying by two decimals together.