Place value to 1,000,000

What is this skill?

In fourth grade children work with whole numbers up to one million. They read and write numbers like 731,304, name the place a digit is in, say what a digit is worth, and compare big numbers with >, < and =. The idea behind all of it is the same one they have used since first grade: every place is worth ten times the place to its right.

That makes the digit 3 in 731,304 worth different amounts depending on where it sits. The 3 in the ten thousands place is worth 30,000, and the 3 in the hundreds place is worth 300. Commas group the digits in threes, which makes long numbers easier to read: ones, tens and hundreds, then the thousands group, then the millions group. To compare two numbers, children line them up and look at the leftmost place where they differ.

Why it matters

Big numbers show up in the world long before children can compute with them: populations, distances, prices, video views. Understanding that a six-digit number is far larger than a five-digit one, and reading it correctly aloud, is basic number sense.

Place value is also the foundation for rounding, multi-digit multiplication and division, decimals and fractions in this same grade. Decimals are simply the same pattern continuing to the right of the ones place. A child who is shaky on what the digits mean will find nearly every other topic this year harder than it needs to be.

Common mistakes

• Confusing the digit with its value. In 6,752 the digit is 6 but the value is 6,000.
• Mixing up the place names, especially ten thousands and hundred thousands, or counting from the left instead of from the right.
• Comparing the last digits instead of starting from the left. 46,877 and 46,977 first differ in the hundreds place, so that is where the comparison is decided.
• Skipping a zero when writing a number from words. “Seven thousand thirty-five” is 7,035, not 735 or 70,035.
• Reading a long number as separate digits instead of in groups, which hides its size.

How to help at home

• Read numbers aloud with the commas: “forty-six thousand, eight hundred seventy-seven.” The commas tell you where to pause.
• Write a number on paper and ask, “Which digit is in the tens place? What is the 4 worth?” Then change one digit and see what happens.
• Collect big numbers from real life: a stadium capacity, a city population, a page count, and have your child put them in order.
• Use a place value chart drawn on a sheet of paper with columns for each place.
• Play “make the biggest number”: draw digits one at a time and place each one in a blank before the next is revealed.

Worked examples

These are real questions from the Tutorsaurus place value to 1,000,000 practice, with the answers worked out.

1. Example 1

   8,100 ? 9,100

   Choices: >, <

   Answer: <. 8,100 < 9,100. Compare the biggest place first.

2. Example 2

   13,754 ? 14,754

   Choices: >, <

   Answer: <. 13,754 < 14,754. Compare the biggest place first.

3. Example 3

   What is the value of the digit 7 in 731,304?

   Choices: 70,000, 7, 700,000, 7,000,000

   Answer: 700,000. The 7 is in the hundred thousands place, so it is worth 700,000.