Place Value & Powers of 10 — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. Which number equals 3.07 × 10³?
A) 307
B) 3,070
C) 30,700
D) 3,007
10³ equals 1,000, so multiply 3.07 by 1,000 by shifting the decimal three places right to get 3,070.
2. In the numbers 640 and 640,000, how many times greater is the value of the 6 in 640,000 than in 640?
A) 10 times
B) 100 times
C) 1,000 times
D) 10,000 times
The 6 in 640,000 is in the hundred-thousands place (600,000) while the 6 in 640 is in the hundreds place (600). Since 600,000 ÷ 600 = 1,000, it is 1,000 times greater.
3. What is (4 × 10⁴) + (8 × 10²) + (5 × 10⁰) in standard form?
A) 40,805
B) 4,850
C) 48,005
D) 40,850
Calculate each term: 4 × 10,000 = 40,000, 8 × 100 = 800, and 5 × 1 = 5. Adding them gives 40,000 + 800 + 5 = 40,805.
4. Which expression is equal to 7,200,000 ÷ 10³?
A) 72
B) 720
C) 7,200
D) 72,000
10³ equals 1,000, and dividing 7,200,000 by 1,000 removes three zeros, giving 7,200.
Part B: Fill in the Blank
Write the correct answer on each line.
1. The digit 5 in 3,500 has a value 100 times the value of the 5 in 35.
The 5 in 3,500 is in the hundreds place (500) and the 5 in 35 is in the ones place (5). Since 500 ÷ 5 = 100, it is 100 times greater.
2. 0.062 × 10⁴ = 620.
10⁴ equals 10,000, and multiplying 0.062 by 10,000 shifts the decimal four places right, giving 620.
3. Write 900,000 as a single digit times a power of 10: 9 × 10⁵.
900,000 has a 9 followed by five zeros, so it equals 9 × 10⁵. The exponent tells you how many zeros follow the digit.
4. (2 × 10⁶) + (7 × 10³) + (1 × 10¹) = 2,007,010.
Calculate each term: 2 × 1,000,000 = 2,000,000, 7 × 1,000 = 7,000, and 1 × 10 = 10. Adding gives 2,000,000 + 7,000 + 10 = 2,007,010.
5. 4,510,000 ÷ 10⁵ = 45.1.
10⁵ equals 100,000, and dividing 4,510,000 by 100,000 shifts the decimal five places left, giving 45.1.