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Number and Place Value - Place Value up to 1,000,000

Grade 4IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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The Place Value Chart: Large numbers up to 1,000,0001,000,000 are organized into periods (Millions, Thousands, and Units), each containing three place values. Imagine a table where the columns from right to left are: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, and Millions. Commas are used to separate these periods, such as in the number 1,000,0001,000,000.

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The Base-Ten Relationship: Our number system follows a base-10 pattern where each place value is exactly 1010 times the value of the place to its right. For example, 1010 Ten Thousands equal 11 Hundred Thousand (10×10,000=100,00010 \times 10,000 = 100,000), and 1010 Hundred Thousands equal 11 Million (10×100,000=1,000,00010 \times 100,000 = 1,000,000).

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Standard, Word, and Expanded Forms: Numbers can be represented in three ways. Standard Form uses digits (523,401523,401). Word Form uses language (five hundred twenty-three thousand, four hundred one). Expanded Form breaks the number down by the value of each digit (500,000+20,000+3,000+400+1500,000 + 20,000 + 3,000 + 400 + 1).

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Digit Value vs. Place: The 'place' is the position of the digit (e.g., the Ten Thousands place), while the 'value' is how much that digit represents based on its place. In the number 876,234876,234, the digit 77 is in the Ten Thousands place, so its value is 70,00070,000.

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Comparing Large Numbers: To compare numbers up to 1,000,0001,000,000, always start comparing from the largest place value (the leftmost digit). If the digits are equal, move to the next place to the right. Use the symbols >> (greater than), << (less than), or == (equal to). For example, 450,000>449,999450,000 > 449,999.

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Rounding to the Nearest Place: To round a number, identify the rounding digit and look at the neighbor to its right. If the neighbor is 55 or more, round the target digit up. If the neighbor is 44 or less, the target digit stays the same, and all digits to the right become zeros. You can visualize this on a number line to see which 'benchmark' number the value is closer to.

📐Formulae

Value=Digit×Place Value Position\text{Value} = \text{Digit} \times \text{Place Value Position}

Expanded Form=(d1×100,000)+(d2×10,000)+(d3×1,000)+(d4×100)+(d5×10)+(d6×1)\text{Expanded Form} = (d_1 \times 100,000) + (d_2 \times 10,000) + (d_3 \times 1,000) + (d_4 \times 100) + (d_5 \times 10) + (d_6 \times 1)

Rounding Rule:If digit to the right≥5,round up\text{Rounding Rule}: \text{If digit to the right} \ge 5, \text{round up}

Rounding Rule:If digit to the right<5,round down/stay\text{Rounding Rule}: \text{If digit to the right} < 5, \text{round down/stay}

💡Examples

Problem 1:

Write the number 804,275804,275 in expanded form and determine the value of the digit in the hundred thousands place.

Solution:

Step 1: Break the number down by its place values. 88 is in the hundred thousands place: 800,000800,000 00 is in the ten thousands place: 00 44 is in the thousands place: 4,0004,000 22 is in the hundreds place: 200200 77 is in the tens place: 7070 55 is in the ones place: 55 Step 2: Combine them for expanded form: 800,000+4,000+200+70+5800,000 + 4,000 + 200 + 70 + 5. Step 3: Identify the value of the digit in the hundred thousands place: 8×100,000=800,0008 \times 100,000 = 800,000.

Explanation:

Expanded form shows the sum of the values of each digit. Even though there is a 00 in the ten thousands place, we usually omit it in the final addition string.

Problem 2:

Round 457,812457,812 to the nearest ten thousand.

Solution:

Step 1: Identify the digit in the ten thousands place. In 457,812457,812, the digit is 55. Step 2: Look at the digit to the immediate right (the thousands place). The digit is 77. Step 3: Since 7≥57 \ge 5, we round the ten thousands digit up from 55 to 66. Step 4: Change all digits to the right of the ten thousands place to zeros. Result: 460,000460,000.

Explanation:

Rounding helps estimate large numbers. Since 457,812457,812 is closer to 460,000460,000 than to 450,000450,000 on a number line, we round up.