How many times greater is 2.523\times 10^{-4}2.523×10

Question

−4
than 2.9\times 10^{-8}2.9×10
−8
? Express your answer using scientific notation.


A
8.7×10−118.7\times 10^{-11}8.7×10
−11


B
8.7×10128.7\times 10^{12}8.7×10
12


C
8.7×1038.7\times 10^38.7×10
3

Answer 1

To determine how many times greater \( 2.523 \times 10^{-4} \) is than \( 2.9 \times 10^{-8} \), we can divide the two numbers:

\[ \text{Factor} = \frac{2.523 \times 10^{-4}}{2.9 \times 10^{-8}} \]

We can split this division into two parts: the coefficients and the powers of ten:

1. Dividing the coefficients: \[ \frac{2.523}{2.9} \approx 0.869 \]

2. Dividing the powers of ten: \[ 10^{-4} \div 10^{-8} = 10^{-4 - (-8)} = 10^{-4 + 8} = 10^{4} \]

Now, we can combine these two results:

\[ \text{Factor} \approx 0.869 \times 10^{4} \]

Next, we convert \( 0.869 \) into scientific notation. Since \( 0.869 = 8.69 \times 10^{-1} \), we can rewrite the factor:

\[ \text{Factor} \approx 8.69 \times 10^{-1} \times 10^{4} = 8.69 \times 10^{3} \]

Rounding \( 8.69 \) to two significant digits gives us \( 8.7 \):

Thus, the final result is:

\[ \text{Factor} \approx 8.7 \times 10^{3} \]

Therefore, the answer is:

\[ \boxed{8.7 \times 10^{3}} \]