The digits 1, 5, and 9 can make many different numbers. The numbers 159, 591, and 915 all use the same digits, but they are not the same value. Why? It all comes down to the position, or place, of each digit.

This idea is called place value. Each spot in a number has a specific value. The digit in that spot tells us how many of that value we have. Let's look at the number 555. It has three 5s, but each one means something different.

Even though the digit is the same, its place changes its value. The first 5 is worth 500, the second is worth 50, and the third is worth just 5. This system allows us to write any number, no matter how big.

To understand bigger numbers, we can use a place value chart. The chart organizes numbers into groups of three places, called periods. You might recognize the ones period (ones, tens, hundreds) and the thousands period (thousands, ten thousands, hundred thousands). Next up is the millions period.

Let's place a large number into the chart, like 2,471,938.

See the commas? They separate the periods, making the number easier to read. To read this number aloud, you say the number in each period, followed by the period's name. So, we say: "Two million, four hundred seventy-one thousand, nine hundred thirty-eight."

Place value also helps us compare numbers. To find out which number is bigger, we don't just count the digits. If the numbers have a different number of digits, the one with more digits is always larger. For example, 10,000 is bigger than 9,999.

What if they have the same number of digits? Let's compare 546,200 and 543,900. Here’s how:

1. Start comparing from the leftmost place.
2. In the hundred thousands place, both numbers have a 5. It's a tie.
3. Move to the next place to the right: the ten thousands place. Both have a 4. Still a tie.
4. Move to the thousands place. The first number has a 6, and the second has a 3.

Since 6 is greater than 3, we know that 546,200 is greater than 543,900. We don't need to check the rest of the digits.

Sometimes we don't need an exact number. An estimate is good enough. This is where rounding comes in. Rounding makes numbers simpler and easier to work with. If a stadium has 48,782 people, you might just say there are "about 49,000 people."

To round a number, you first need to know which place you are rounding to. Let's round 48,782 to the nearest thousand.

1. Find the rounding place. The thousands place has an 8 in it: 48,782.

2. Look at the digit to its right. The digit is 7.

3. Apply the rule. If the digit to the right is 5 or more (5, 6, 7, 8, or 9), you round up. If it's 4 or less (4, 3, 2, 1, or 0), you keep the digit in the rounding place the same. Since 7 is 5 or more, we round the 8 up to a 9.

4. Change the rest of the digits. All digits to the right of the rounding place become zeros.

Let's try one more. Round 321,450 to the nearest ten thousand.

1. The ten thousands digit is 2: 321,450.
2. The digit to its right is 1.
3. 1 is less than 5, so we keep the 2 as it is.
4. Change all digits to the right to zeros.

The number 321,450 rounded to the nearest ten thousand is 320,000.

Now that you have a handle on place value, comparing, and rounding, you're ready to work with all sorts of numbers, big and small.