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Decimals – Help With Multiplying Decimals TutorGiant Multiplying regular numbers is similar to multiplying decimals. When multiplying decimals by 10’s, 100’s, or 1000’s, we simply move the decimal in the answer to the right according to the number of zeros (i.e. 2 zeros in 100, 3 zeros in 1000) the decimal is being multiplied by. For example, in 9.5 x 10 we can see that there is 1 zero in the number 10. So, we move the decimal 1 space to the right in the answer. The answer becomes 95.0, or 95. If we had 9.5 x 100 we can see that there are 2 zeros in 100, so we move the decimal 2 spaces to the right. The answer becomes 950.0 or 950 (we don’t always have to show the decimal and a zero). When multiplying numbers that are not powers of ten, we must use a different strategy. Let’s multiply 5 x 0.6 by first treating them as if they were integers. 5 x 6 = 30 Next, we’ll count how many decimal places are to the right of the decimal place. The only digit to the right of the decimal place is the 6 (i.e. 0.6). Since the answer of 5 x 6 = 30 and we know that there was 1 digit to the right of the decimal place in the question, we will also have 1 digit to the right of the decimal in the answer. So, 5 x 6 = 30 Then 5 x 0.6 = 3.0 (Here we have 1 digit to the right of the decimal, the zero). When we multiply decimals, we must remember that: one digit to the right of the decimal in the question= 1 digit to the right of the decimal in the answer. Let’s try to multiply decimals with 2 digits to the right of in the question. We will multiply 3 x 0.25 and use the same strategy as above. Here, we can see that there are 2 digits to the right of the decimal (i.e. 2 and 5). So, 3 x 25 = 75 Then, 3 x 0.25 = 0.75 (Two digits to the right of the decimal!) When we multiply decimals, we must remember that: two digits to the right of the decimal in the question = 2 digits to the right of the decimal in the answer. The same rule applies for 3 digits, 4 digits, and so on. If we were to multiply 42.3 x 57.61, you would know that the answer will have 3 digits to the right of the decimal (i.e. the 3, 6, and 1 are to the right of the decimal). This is a great way for students to check their work when multiplying decimals. Students must remember to pay attention to the number of zeros when multiplying decimals with powers of ten. They should also remember to count the number of digits to the right of the decimals in questions in order to know where to put the decimal in the answer.
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