How to Decompose Numbers

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Decomposing numbers sometimes mean that you're just showing the place value of a given term. Decompose numbers with help from a longtime math teacher in this free video clip.

Part of the Video Series: Math Tips
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Video Transcript

Hi, my name is Marija. I'm a mathematician and today I'm going to show you how to decompose numbers. So, if you're in the lower level grades, then to decompose a number is going to mean just to show its place value. So, if I have the number four hundred and twenty-five, to decompose it would mean four is in the hundreds place, so I would take that four and rewrite it as four hundred to show its value. Plus, since two is in the tens place, I would write it as twenty to show its value. And five is in the ones place, so I would write plus five. So, if you're in elementary school, that's what they might mean by decomposing numbers. However, if you're in middle or high school, to decompose a number means to break it down into its prime factors. So, it's the same thing as doing prime factorization. So, if I have the number twenty-seven and I want to decompose it, I'm going to think of two factors of twenty-seven, and the first ones that come to mind for me are nine and three. And what I'm going to do is circle any factor that's prime. So, three is prime. I'm going to circle it, and I'm going to continue to break down another factor. So, nine breaks down into three and three, both of which are prime, so I'm going to circle them both. Now, I'm done breaking down the numbers. All my branches are circled off. So, I'm going to rewrite this as three times three times three. And I could rewrite that, that's the same thing as three cubed, because it's three multiplied by itself three times. So, the decomposition of twenty-seven would be three cubed. My name is Marija, and I just showed you how to decompose a number.


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