Place Value & Powers of 10 — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A number has a 6 in the ten-thousands place. Its value from that digit alone is 6 × 10 to what power?
A) 10³
B) 10⁴
C) 10⁵
D) 10⁶
The ten-thousands place is 10,000, which equals 10⁴. So the digit 6 in that place has a value of 6 × 10⁴ = 60,000.
2. Which shows 50,300 written as two terms with powers of 10?
A) (5 × 10⁴) + (3 × 10³)
B) (5 × 10⁴) + (3 × 10²)
C) (5 × 10³) + (3 × 10²)
D) (5 × 10⁵) + (3 × 10²)
50,300 breaks into 50,000 + 300. Since 50,000 = 5 × 10⁴ and 300 = 3 × 10², the expanded form is (5 × 10⁴) + (3 × 10²).
3. 0.25 × 10⁵ equals which value?
A) 250
B) 2,500
C) 25,000
D) 250,000
10⁵ equals 100,000, and multiplying 0.25 by 100,000 shifts the decimal five places right, giving 25,000.
4. Sam says 8 × 10⁴ is the same as 80 × 10³. Is he correct, and why?
A) No — 80 × 10³ = 800,000
B) Yes — both equal 80,000
C) No — 8 × 10⁴ = 8,000
D) Yes — both equal 800,000
8 × 10⁴ = 8 × 10,000 = 80,000 and 80 × 10³ = 80 × 1,000 = 80,000. Both expressions equal 80,000, so Sam is correct.
Part B: Fill in the Blank
Write the correct answer on each line.
1. Write 2,400,000 as 24 times a power of 10: 24 × 10 to the power of 5.
2,400,000 ÷ 24 = 100,000, and 100,000 = 10⁵, so 2,400,000 = 24 × 10⁵ and the exponent is 5.
2. The digit 8 in 830,000 has a value that is 100 times the value of the 8 in 8,300.
The 8 in 830,000 is in the hundred-thousands place (800,000) and the 8 in 8,300 is in the thousands place (8,000). Since 800,000 ÷ 8,000 = 100, it is 100 times greater.
3. (9 × 10⁵) + (4 × 10²) + (6 × 10⁰) = 900,406.
Calculate each term: 9 × 100,000 = 900,000, 4 × 100 = 400, and 6 × 1 = 6. Adding gives 900,000 + 400 + 6 = 900,406.
4. 1.35 × 10⁴ = 13,500.
10⁴ equals 10,000, and multiplying 1.35 by 10,000 shifts the decimal four places right, giving 13,500.
5. 6,090,000 ÷ 10³ = 6,090.
10³ equals 1,000, and dividing 6,090,000 by 1,000 removes three zeros, giving 6,090.