Question

Which of these shows a correct pattern of multiplying by powers of ten?
A.
58 × 10 = 580
58 × 102 = 5,800
58 × 103 = 58,000
58 × 104 = 580,000
B.
36 × 10 = 360
36 × 102 = 3,600
36 × 103 = 36,000
36 × 104 = 3,600,000
C.
12 × 10 = 1,200
12 × 102 = 12,000
12 × 103 = 120,000
12 × 104 = 1,200,000
D.
60 × 10 = 600
60 × 102 = 60,000
60 × 103 = 600,000
60 × 104 = 6,000,000

Answer 1

To determine which option shows the correct pattern of multiplying by powers of ten, we need to understand that multiplying a number by 10^n (where n is the power) effectively shifts the decimal point n places to the right.

Let's evaluate each option:

**A:**
- \( 58 \times 10^1 = 580 \) (correct)
- \( 58 \times 10^2 = 5,800 \) (correct)
- \( 58 \times 10^3 = 58,000 \) (correct; this should be 58,000)
- \( 58 \times 10^4 = 580,000 \) (correct)

**B:**
- \( 36 \times 10^1 = 360 \) (correct)
- \( 36 \times 10^2 = 3,600 \) (correct)
- \( 36 \times 10^3 = 36,000 \) (correct)
- \( 36 \times 10^4 = 3,600,000 \) (incorrect; should be 360,000)

**C:**
- \( 12 \times 10^1 = 120 \) (incorrect; should be 120)
- \( 12 \times 10^2 = 12,000 \) (correct)
- \( 12 \times 10^3 = 120,000 \) (correct)
- \( 12 \times 10^4 = 1,200,000 \) (correct)

**D:**
- \( 60 \times 10^1 = 600 \) (correct)
- \( 60 \times 10^2 = 6,000 \) (incorrect; should be 6,000)
- \( 60 \times 10^3 = 600,000 \) (incorrect; should be 600,000)
- \( 60 \times 10^4 = 6,000,000 \) (incorrect; should be 6,000,000)

Based on this analysis, **option A** shows the correct pattern of multiplying by powers of ten. The others either contain mistakes or deviate from the correct decimal place shifts after multiplying by the respective powers of ten.