Question

order the set of numbers from greatest to least.
$5.72 \times 10^3$, $8.15 \times 10^2$, $7.1 \times 10^3$, $9.51 \times 10^2$
a
$5.72 \times 10^3$, $7.1 \times 10^3$, $9.51 \times 10^2$, $8.15 \times 10^2$
b
$5.72 \times 10^3$, $7.1 \times 10^3$, $8.15 \times 10^2$, $9.51 \times 10^2$
c
$7.1 \times 10^3$, $5.72 \times 10^3$, $9.51 \times 10^2$, $8.15 \times 10^2$
d
$9.51 \times 10^2$, $8.15 \times 10^2$, $5.72 \times 10^3$, $7.1 \times 10^3$

Explanation:

Step1: Analyze the exponents of 10

Numbers with \(10^3\) (thousands place multiplier) are larger than those with \(10^2\) (hundreds place multiplier) because \(10^3 = 1000\) and \(10^2=100\), so \(a\times10^3>b\times10^2\) for any positive \(a,b\). So first, group numbers by their exponents:

• \(10^3\) group: \(5.72\times 10^3\), \(7.1\times 10^3\)
• \(10^2\) group: \(8.15\times 10^2\), \(9.51\times 10^2\)

Step2: Compare numbers within \(10^3\) group

For numbers with the same exponent (\(10^3\)), compare the coefficients. The coefficient of \(5.72\times 10^3\) is \(5.72\) and for \(7.1\times 10^3\) is \(7.1\). Since \(7.1>5.72\), we have \(7.1\times 10^3 > 5.72\times 10^3\).

Step3: Compare numbers within \(10^2\) group

For numbers with the same exponent (\(10^2\)), compare the coefficients. The coefficient of \(8.15\times 10^2\) is \(8.15\) and for \(9.51\times 10^2\) is \(9.51\). Since \(9.51 > 8.15\), we have \(9.51\times 10^2>8.15\times 10^2\).

Step4: Order from greatest to least

Combining the groups (since \(10^3\) group is larger than \(10^2\) group), the order from greatest to least is: \(7.1\times 10^3\), \(5.72\times 10^3\), \(9.51\times 10^2\), \(8.15\times 10^2\). Now check the options:

• Option A: \(5.72\times 10^3, 7.1\times 10^3, 9.51\times 10^2, 8.15\times 10^2\) → Incorrect (since \(7.1\times 10^3>5.72\times 10^3\))
• Option B: \(5.72\times 10^3, 7.1\times 10^3, 8.15\times 10^2, 9.51\times 10^2\) → Incorrect (since \(9.51\times 10^2>8.15\times 10^2\))
• Option C: \(7.1\times 10^3, 5.72\times 10^3, 9.51\times 10^2, 8.15\times 10^2\) → Correct (matches our order)
• Option D: \(9.51\times 10^2, 8.15\times 10^2, 5.72\times 10^3, 7.1\times 10^3\) → Incorrect (since \(10^3\) group is larger than \(10^2\) group)

Answer:

C. \(7.1 \times 10^3, 5.72 \times 10^3, 9.51 \times 10^2, 8.15 \times 10^2\)