## One Step Closer to Full Multiple Digit Multiplication!

We’ve seen how to multiply two digit numbers in some detail, but the case of the three digit number should make this seem a little more general. If you understand how to multiply a three digit number by a single digit, you’ll not only understand how to multiply a number of any length, but you’ll have mastered one of the core parts of the general algorithm for multiple digit multiplication. Ready? Let’s go!

## Multiplying Three Digits of Place Value

Like our prior examples, multiplying three digit numbers by a single digit is an exercise in applying our multiplication facts individually to each place value. In this case, we’re looking at a number that has a ones, tens and hundreds place value, so we’ll have exactly three multiplications that come into play.

Just like with our two digit example, some of those intermediate multiplication steps will likely yield a number that has a two digit number, so we’ll potentially carry then tens place from that step back up into the upper multiplicand. Because of this carrying process, these steps across the place value aren’t strictly just multiplying… We occasionally need to add that carried place value as we progress.

The best way to understand this is to see the steps in action…