Place Value Basics - Answer Sheet

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📚 Part 1: Place Value Identification - Answers

1. In the number 2,847,593, what is the place value of the digit 4?

Answer: Ten thousands place

Explanation: The digit 4 is in the fifth position from the right (ten thousands), so its value is 40,000.

2. In the number 156.73, what is the value of the digit 7?

Answer: 7 tenths or 0.7

Explanation: The digit 7 is in the first position after the decimal point (tenths place), so its value is 7/10 or 0.7.

3. What is the place value of 9 in the number 3,921,456?

Answer: Hundred thousands place

Explanation: The digit 9 is in the sixth position from the right, making its value 900,000.

4. In 47.85, what is the value of the digit 5?

Answer: 5 hundredths or 0.05

Explanation: The digit 5 is in the second position after the decimal point (hundredths place), so its value is 5/100 or 0.05.

✏️ Part 2: Number Writing and Expanded Form - Answers

5. Write 4,526,318 in expanded form.

Answer: 4,000,000 + 500,000 + 20,000 + 6,000 + 300 + 10 + 8

Explanation: Each digit is multiplied by its place value: 4 millions, 5 hundred thousands, 2 ten thousands, 6 thousands, 3 hundreds, 1 ten, and 8 ones.

6. What number is represented by: 3 × 100,000 + 7 × 10,000 + 2 × 1,000 + 9 × 100 + 4 × 10 + 6 × 1?

Answer: 372,946

Explanation: 300,000 + 70,000 + 2,000 + 900 + 40 + 6 = 372,946

7. Write 25.67 in expanded form using decimals.

Answer: 2 × 10 + 5 × 1 + 6 × 0.1 + 7 × 0.01 or 20 + 5 + 0.6 + 0.07

Explanation: The whole number part uses standard place values, while decimal places use fractional place values (tenths and hundredths).

8. Round 3,847,291 to the nearest hundred thousand and explain your reasoning.

Answer: 3,800,000

Explanation: Look at the ten thousands digit (4). Since 4 < 5, we round down. The hundred thousands digit (8) stays the same, and all digits to the right become zero.

🎯 Part 3: Problem Solving and Application - Answers

9. A school has 1,247 students. If the digit in the hundreds place increased by 3, how many students would the school have?

Answer: 1,547 students

Explanation: The hundreds digit is 2. Increasing it by 3 makes it 5, changing the number from 1,247 to 1,547 (an increase of 300 students).

10. Compare these numbers and explain which is larger: 2.34 or 2.340

Answer: They are equal (2.34 = 2.340)

Explanation: Adding zeros after the last decimal place doesn't change the value. Both represent 2 + 3 tenths + 4 hundredths.

11. Extension: Express 4.7 × 10³ in standard form and identify the place value of each digit.

Answer: 4,700

Explanation: 4.7 × 10³ = 4.7 × 1,000 = 4,700. The 4 is in the thousands place (value 4,000), the 7 is in the hundreds place (value 700), and the zeros are placeholders in tens and ones places.

12. Real-world application: New Zealand's population is approximately 5.2 million. Write this number in standard form and identify the place value of the digit 5.

Answer: 5,200,000 and the 5 is in the millions place

Explanation: 5.2 million = 5,200,000. The digit 5 represents 5 million, showing its position determines it represents 5,000,000 rather than just 5.