Question

0.65 × 10 = 6.5
0.65 × 10² = 65
0.65 × 10³ = 650
if this pattern continues, what is the result of 0.65 × 10⁵?
a 0.065
b 65
c 6,500
d 65,000

Explanation:

Step1: Identify the pattern

When multiplying a decimal by \(10^n\), the decimal point moves \(n\) places to the right. For example, \(0.65\times10^1 = 6.5\) (moved 1 place right), \(0.65\times10^2=65\) (moved 2 places right), \(0.65\times10^3 = 650\) (moved 3 places right).

Step2: Apply the pattern to \(10^5\)

For \(0.65\times10^5\), \(n = 5\), so we move the decimal point in \(0.65\) 5 places to the right.

• Moving 1 place: \(6.5\)
• Moving 2 places: \(65\)
• Moving 3 places: \(650\)
• Moving 4 places: \(6500\)
• Moving 5 places: \(65000\)

Answer:

D. 65,000