Answer:
5 × 10³ = 5000
Step-by-step explanation:
Standard Form (also called "Scientific notation") is written in the form of
[tex]a \times 10^n[/tex] , where [tex]1\leq a < 10[/tex] and n is any positive or negative whole number.
Given:
- Lucy's latest score: 3 × 10⁷
- Lucy's first score: 6 × 10³
To calculate how many times as many points is Lucy's last score as her first score, divide her latest score by her first score:
[tex]\implies \dfrac{3 \times 10^7}{6 \times 10^3}[/tex]
[tex]\implies \dfrac{3}{6} \times \dfrac{10^7}{10^3}[/tex]
[tex]\implies 0.5 \times \dfrac{10^7}{10^3}[/tex]
[tex]\textsf{Apply the quotient rule of exponents} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 0.5 \times 10^{7-3}[/tex]
[tex]\implies 0.5 \times 10^{4}[/tex]
In standard form:
[tex]\implies 5 \times 10^{3}[/tex]
Therefore:
[tex]\begin{aligned} \implies 5 \times 10^{3} & =5 \times 10 \times 10 \times 10\\ & =5 \times 1000 \\& =5000 \end{aligned}[/tex]
Learn more about exponent rules here:
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