Multiplying Decimal Numbers

Student: I remember that a decimal number is a number that is in between two integers.

Mentor: That's right, but do you remember how decimal numbers are written?

Student: They have a decimal point and then some more numbers to show how much bigger than the integer they are.

Mentor: That's very good. What do those numbers after the decimal point represent?

Student: It's like a fraction where the denominator is a power of ten. For example, twenty-five hundredths is written as 0.25 or .25 as a decimal.

Mentor: Great example! Now do you recall how to multiply decimal numbers?

Student: It's like multiplying regular numbers only you have to add the decimal point when you're done.

Mentor: Good, do you remember how to determine where the decimal goes?

Student: I think that you count all the decimal places on the numbers that you multiplied together and that's how many places are in the answer.

Mentor: Right. So if I multiplied 0.25 by 0.1, how many decimal places would the final answer have?

Student: Three!

Mentor: Okay, so what is that result?

Student: Um, hang on... it's .025?

Mentor: Good. Now who can tell me how to multiply decimal numbers if they're greater than 1?

Student: Its the same as multiplying with smaller decimal numbers, you count the number of decimal places in the original problem and that is how many there are in the answer.

Mentor: That's correct too but you do need to be careful not to count trailing zeros. For instance, if you have 1.25 multiplied by 1.50 how many decimal places should be in your final answer?

Student: There would only be three because the number 1.50 has a trailing zero so that shouldn't be counted as a decimal place. So the final answer is 1.875.

Mentor: Exactly. What about multiplying 1.25 by 1.05?

Student: There would be four decimal places because the 0 in 1.05 is not a trailing zero. The answer to 1.25 x 1.05 is 1.3125.

Mentor: Let's try one more. What if you have 1.2 x 2.5?

Student: There would be two decimal places because there's no trailing zero. The answer is 3.00, which is the same as 3.

Mentor: Sounds like you've got the hang of it!