What is the smallest eight-digit number?
We know we need to find the smallest eight-digit number, but what are the digits worth in an eight-digit number? Let’s draw a place value grid to help us. There we are, eight columns for eight digits. We know the smallest value column is the ones column. That’s the column on the right. Next one along is our tens column, and then our hundreds column. We could refer to this group of three as being our ones, our hundreds, tens, and ones. To the left of our hundreds column is our thousands column. Then, our tens of thousands column. And next, our hundred thousands column. This group of three is our thousands group, hundred thousands, ten thousands, and thousands.
Our next group is a group of two. It would be a group of three, but we’re talking about an eight-digit number, so it only needs to be a group of two. And, this is our millions group. We have our millions column and our tens of millions column. And, we know that to help us read large numbers like this, we often use commas in between each of the groups or a small space to help us read the millions, thousands, and ones.
Now, the question asks to find the smallest eight-digit number. Each of the eight places in this number can have a different digit in it. But, if we want to make the smallest eight-digit number, then we’d need to put the smallest digit possible into each column. How many ones is the smallest possible number of ones? Well, the answer is zero. And, the same goes for the number of tens, the number of hundreds, thousands, ten thousands, hundred thousands, millions, and ten millions. Zero is the smallest digit that we can use in each column. But, if we try to read this number, it’s not an eight-digit number, it’s just zero because we view zero in all the columns.
Now, all of the columns can have a zero in them apart from the first one. We need to change this digit to something other than zero. We can keep all the other zeroes where they are. What digit should we use if we want to keep this number as small as possible? If we can’t use zero, we’d better use the next smallest digit, which is one. Now, we have a number that is an eight-digit number. And, this is the smallest possible eight-digit number that we could write. We used zero where we could, and where we couldn’t use a zero, we used the next smallest digit, which was one.
Now, we can write our eight-digit number using commas to separate each group. The number of millions that we have is 10. The number of thousands that we have is zero. And, the number of hundreds, tens, and ones that we have in our ones group is also zero. Obviously, we don’t read the numbers 10 millions, zero thousands, zero ones. We just say 10 million. We made the smallest eight-digit number by using the smallest possible digit in seven of the places. But to keep our number from not being zero, we had to use one in the 10 millions place. Our smallest eight-digit number is 10 million.