5.3+Multiplying+Decimals

Section 5.3 - Multiplying Decimals
When you multiply whole numbers, you line them up on the right (ones place) and multiply away, adding the columns to get the final product.

The process for multiplying decimals is similar, in that you line up the numbers on the right, but different, because they are no longer necessarily in place value columns. That doesn't matter.

Line up the numbers by the digits on the furthest right (smallest place value), rather than lining up the decimals. Multiply just like you would whole numbers. Then worry about putting the decimal in the correct place in the answer.

To place the decimal point in the answer, count the total number of digits after the decimal point in each of the numbers being multiplied. That is how many digits should be after the decimal point in the answer as well!



Sometimes there are not enough digits in the answer to move the decimal point over. In this case, add zeroes as placeholders so that there are enough. The example below shows that.



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 * Powers of Ten**

10 times 7 is 70. 10 times 0.7 is 7. You would do the problem the same way according to the instructions above, but you would need to move the decimal point over one place in the answer. If you practice a few of these, you will find that multiplying any decimal number by ten moves the decimal over one place. Multiply it by 100 and it moves over two places. If you are multiplying a decimal number by a power of ten (10, 100, 1000, etc.), you just make the number larger by moving the decimal over as many places as there are zeroes in the power of ten. **Note**: You may need to add more zeroes as place holders in order to do that!



If you are multiplying decimal numbers and you get the decimal in the wrong place, you will be off by a factor of 10 or 100 or 1000. Just moving the decimal one place will change your answer by ten times the value. It would be a good idea, then, to quickly estimate what you think the answer should be. Ignore the decimals and multiply the whole numbers, or front-end round each factor and multiply. If your estimate is close to the answer you got - you probably did it right. If it is off by ten times, you moved the decimal point to the wrong place.


 * What about with variables?**

No differences in the rules. Multiply the coefficients by the coefficients and the variables by the variables.


 * Chapter Five Practice Problems**

**Where to from here?**
5.1 Decimals and Fractions 5.2 Adding and Subtracting Decimals 5.3 Multiplying Decimals 5.4 Dividing Decimals 5.5 Application Problems with Decimals Chapter Five Summary Chapter Five Homework