Question

which expression has the greatest value?
a. $0.045 \times 10^5$
b. $4.5 \times 10^4$
c. $45,000 \times 10^{-4}$
d. $0.45 \times 10^{-6}$

Explanation:

Step1: Calculate value of Option A

We know that \(10^{5}=100000\), so \(0.045\times10^{5}=0.045\times100000 = 4500\)

Step2: Calculate value of Option B

We know that \(10^{4} = 10000\), so \(4.5\times10^{4}=4.5\times10000=45000\)

Step3: Calculate value of Option C

First, \(45000\times10^{- 4}\), and \(10^{-4}=\frac{1}{10000}\), so \(45000\times\frac{1}{10000} = 4.5\)

Step4: Calculate value of Option D

We know that \(10^{-6}=\frac{1}{1000000}\), so \(0.45\times10^{-6}=0.45\times\frac{1}{1000000}=4.5\times10^{-7}=0.00000045\)

Step5: Compare the values

We have values: Option A: \(4500\), Option B: \(45000\), Option C: \(4.5\), Option D: \(0.00000045\). By comparing these values \(45000>4500 > 4.5>0.00000045\)

Answer:

B. \(4.5\times10^{4}\)