Place value: comparing same digit in different places

I've written out two numbers here, and they both contain 4. They each have 4 as a digit, and I want to think about what the values of these 4's are and to actually compare them. So I encourage you to pause the video and try that out on your own. So let's look at the two 4's here. So in 110,413, I have a 4 right over here. And what does that actually represent? Well, this is the ones place. You have three 1's. You have one 10's. And the 4 is in the hundreds place. You have four 100's. So this 4 literally represents 4 times 100, or 400. Now, what about this 4? Well, once again, you have zero 1's. You have five 10's. You have three 100's. And you have four 1,000's. So this literally represents 4 times 1,000, which is 4,000. So we can now compare the two. The 4 in 110,413 is 1/10 the value of the 4 in 54,350. And it makes complete sense. This 4 is one place to the right of this 4. This 4 is in the thousands. The magenta-circled 4 is in the hundreds. So every time we move a place value to the right, each increment represents 1/10 as much, assuming we have the same digit. So a 4 in thousands is 4,000. A 4 in hundreds would be 1/10 as much. A 4 in the tens would be 1/10 as much as that. So we could write a sentence. Let me write it this way. The value of the 4 in this number is 1/10 the value of the 4 in this number. I know it's a little bit weird sentence. The value of the 4 in 110,413 is 1/10 the value of the 4 in 54,350.