Place Value for 5th Grade: Master the Foundation of Numbers with Confidence

Place value is the foundation of our entire number system. Every digit in a number has a specific value that depends entirely on its position—where it sits in the number. In Grade 5, students extend their understanding of place value to much larger whole numbers: hundreds of thousands, millions, and beyond. Without a solid grasp of place value, students struggle with reading numbers, comparing them, rounding, and performing operations accurately.

Understanding place value helps students make sense of real-world situations: populations of cities, distances between planets, prices of homes, and quantities in science. When we say a city has 834,729 residents, each digit tells us something important. The 8 represents 800,000 people—eight hundred thousands. The 3 represents 30,000. The 4 represents 4,000. The 7 represents 700. The 2 represents 20. The 9 represents 9. Place value allows us to communicate large numbers efficiently and precisely.

DETAILED EXPLANATION

Our number system is base-ten (decimal). This means each place value is 10 times the value of the place to its right. Moving from right to left, we have:

Ones (1) — Tens (10) — Hundreds (100) — Thousands (1,000) — Ten Thousands (10,000) — Hundred Thousands (100,000) — Millions (1,000,000)

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The value of any digit equals the digit multiplied by its place value. For example, in the number 45,678:

• The 4 is in the ten thousands place, so its value is \(4 \times 10{,}000 = 40{,}000\)

• The 5 is in the thousands place, so its value is \(5 \times 1{,}000 = 5{,}000\)

• The 6 is in the hundreds place, so its value is \(6 \times 100 = 600\)

• The 7 is in the tens place, so its value is \(7 \times 10 = 70\)

• The 8 is in the ones place, so its value is \(8 \times 1 = 8\)

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We use commas to separate groups of three digits (thousands, millions) to make large numbers easier to read. The number 1,234,567 has three groups: 1 (millions), 234 (thousands), and 567 (ones).

Expanded form shows a number as the sum of each digit’s value. For example, \(52{,}341 = 50{,}000 + 2{,}000 + 300 + 40 + 1\). This form helps students see exactly what each digit contributes to the total.

WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

In the number 834,729, what is the value of the 7?

Solutions:

Step 1: Identify the place of each digit. Working from right to left: 9 is in the ones place, 2 is in the tens place, 7 is in the hundreds place, 4 is in the thousands place, 3 is in the ten thousands place, and 8 is in the hundred thousands place.

Step 2: The digit 7 is in the hundreds place. The hundreds place has a value of 100.

Step 3: Calculate the value: Value = digit × place value = \(7 \times 100 = 700\).

Step 4: The 7 represents 700 in the number 834,729.

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Answer: The value of the 7 is 700.

Example 2

A town’s population is 52,341. Write this number in expanded form.

Solutions:

Step 1: Identify each digit and its place value. The number 52,341 has five digits. From left to right: 5 is in the ten thousands place (value 50,000), 2 is in the thousands place (value 2,000), 3 is in the hundreds place (value 300), 4 is in the tens place (value 40), and 1 is in the ones place (value 1).

Step 2: Write each digit’s value as a separate term: 50,000, 2,000, 300, 40, and 1.

Step 3: Write the expanded form as a sum: \(52{,}341 = 50{,}000 + 2{,}000 + 300 + 40 + 1\).

Step 4: Verify: \(50{,}000 + 2{,}000 + 300 + 40 + 1 = 52{,}341\). ✓

Answer: \(52{,}341 = 50{,}000 + 2{,}000 + 300 + 40 + 1\)

Example 3

In which number does the 4 have the greatest value?

A) 4,521 B) 24,891 C) 89,426 D) 126,440

Solutions:

Step 1: For each number, identify the place of the digit 4 and calculate its value.

Step 2: In A (4,521): The 4 is in the thousands place. Value = \(4 \times 1{,}000 = 4{,}000\).

Step 3: In B (24,891): The 4 is in the thousands place. Value = \(4 \times 1{,}000 = 4{,}000\).

Step 4: In C (89,426): The 4 is in the hundreds place. Value = \(4 \times 100 = 400\).

Step 5: In D (126,440): The first 4 is in the hundreds place. Value = \(4 \times 100 = 400\). (The second 4 is in the tens place: \(4 \times 10 = 40\).)

Step 6: Compare the values: 4,000 (A and B) > 400 (C and D). Both A and B have 4 with the greatest value of 4,000.

Answer: Both A and B have the digit 4 with value 4,000, which is the greatest among the choices.

Example 4

What number has 8 ten thousands, 4 thousands, 2 hundreds, 6 tens, and 1 one?

Solutions:

Step 1: Write each value: 8 ten thousands = 80,000; 4 thousands = 4,000; 2 hundreds = 200; 6 tens = 60; 1 one = 1.

Step 2: Add them together: \(80{,}000 + 4{,}000 + 200 + 60 + 1 = 84{,}261\).

Step 3: Verify by reading the number: 84,261 has 8 in ten thousands, 4 in thousands, 2 in hundreds, 6 in tens, and 1 in ones. ✓

Answer: 84,261