Middle school math teachers and online math tutors know that mathematics is the subject that helps young students understand the world around them more than any other. Even though the students often don’t realize it themselves, as they begin exploring more complex mathematical concepts, such as multiplication and division of decimals by factors of ten, they are learning to use the tools that will help them solve everyday problems throughout their lives.
Most of us are most comfortable multiplying or dividing something if it is a multiple of ten. Why do you think that is? Is there anything fundamentally different about these numbers when compared to others? Are these operations less complicated or more intuitive than others we have learned – and forgotten – long ago?
Let’s take a look at some foundational decimal arithmetic, focusing on how students learn to divide and multiply decimals by factors of ten, to see if the answers to these questions can become clearer.
Multiplying and Dividing Decimals by 10, 100, and 1000
Multiplying and dividing decimals by factors of ten is one of the most fundamental skills a middle school math student will learn. They are operations that are built upon understanding place value. What that means is that to perform these operations correctly, we need to understand decimal points.
When we multiply or divide any number by 10, 100, or 1000, are essentially moving the decimal point to the right, or the left. Without adequately understanding place value, we will not know where are decimal point should be, and, therefore, we are likely to make mistakes when moving the decimal point.
We can demonstrate this better by looking at examples of dividing and multiplying decimals by 10, 100, and 1000 separately.
Multiplying and Dividing Decimals by 10
If we want to multiply or divide any decimal by 10, we simply move the decimal one place to the right or the left. Take the number 2.45. If we multiply 2.45 by 10, we can move our decimal one space to the right, giving us the answer 24.5. Similarly, if we want to divide our number by ten, we will move the decimal in 2.45 one space to the left, leaving us with 0.245.
We can (and should) perform regular multiplication and division on these numbers to verify that these answers are correct.
We now know that to divide decimals by 10, we will move the decimal to the left, and if we are multiplying that decimal by 10, we will move it to the right. We will use the same approach to divide decimals by 100, and 1000.
Multiplying and Dividing Decimals by 100
Multiplying or dividing a decimal by 100 is very similar to multiplying and dividing a decimal by 10. As above, we will move the decimal to the right or the left, but this time, instead of shifting the decimal one space either way, we will shift it two spaces either way.
Taking the same number as we used above, we can divide 2.45 by 100 to get 0.0245. If we want to multiply 2.45 by 100, we can move the decimal to the right, giving us 245.
Multiplying and Dividing Decimals by 1000
Just like when we multiply and divide decimals by 10, and 100, when we are using the number 1000, we must move the decimal point to either the right or left. This time, the decimals will be moving three places to the left or right.
Using the same example as above, we can multiply 2.45 by 1000, moving the decimal three places to the right, and we get 2450. We can also move the decimal three spaces to the left, giving us the answer to the problem of what is 2.45 divided by 1000. This answer is, of course, 0.00245.
Multiply Your Child’s Potential with OMC
Multiplication and division of decimals by factors of ten play a vital role in any young middle school math student’s progress in class and overall mathematical development. Understanding these operations allows students to work with decimals more effectively, setting them up with the necessary tools to solve real-world problems.
If you want to help ensure your child can solve these problems and reach their mathematical potential, the Online Math Center is the tutoring platform for you.
We offer highly focused 1-1 tutoring classes for students of all ages, as well as specific prep courses for math competitions, and the Math SAT. Our experienced tutors boast years of experience and extensive expertise, and our small class sizes ensure your child is granted more attention than possible in regular school classrooms.