Which of these shows a correct pattern of multiplying by powers of ten?

Question

A.
12 × 10 = 1,200
12 × 102 = 12,000
12 × 103 = 120,000
12 × 104 = 1,200,000
B.
60 × 10 = 600
60 × 102 = 60,000
60 × 103 = 600,000
60 × 104 = 6,000,000
C.
58 × 10 = 580
58 × 102 = 5,800
58 × 103 = 58,000
58 × 104 = 580,000
D.
36 × 10 = 360
36 × 102 = 3,600
36 × 103 = 36,000
36 × 104 = 3,600,000

Answer 1

To determine which option shows a correct pattern of multiplying by powers of ten, let's review how multiplying by powers of ten works.

When you multiply a number by powers of ten:

• Multiplying by \(10^1\) (or 10) shifts the decimal point one place to the right.
• Multiplying by \(10^2\) (or 100) shifts the decimal point two places to the right.
• Multiplying by \(10^3\) (or 1000) shifts the decimal point three places to the right.
• Multiplying by \(10^4\) (or 10,000) shifts the decimal point four places to the right.

Now, let's examine each option to see if they follow this rule:

A.

• \(12 \times 10 = 120\) (not 1,200)
• \(12 \times 10^2 = 1,200\) (incorrect)
• \(12 \times 10^3 = 12,000\) (correct)
• \(12 \times 10^4 = 120,000\) (correct)

This option incorrectly calculates the first multiplication.

B.

• \(60 \times 10 = 600\) (correct)
• \(60 \times 10^2 = 6,000\) (not 60,000)
• \(60 \times 10^3 = 600,000\) (correct)
• \(60 \times 10^4 = 6,000,000\) (correct)

This option incorrectly calculates the second multiplication.

C.

• \(58 \times 10 = 580\) (correct)
• \(58 \times 10^2 = 5,800\) (correct)
• \(58 \times 10^3 = 58,000\) (correct)
• \(58 \times 10^4 = 580,000\) (correct)

All calculations in this option are correct.

D.

• \(36 \times 10 = 360\) (correct)
• \(36 \times 10^2 = 3,600\) (correct)
• \(36 \times 10^3 = 36,000\) (correct)
• \(36 \times 10^4 = 360,000\) (not 3,600,000)

This option incorrectly calculates the last multiplication.

The correct option that shows a proper pattern of multiplying by powers of ten is C.