How many times greater is 1.008 x 10^-4 than 4.2 x 10^-6 ? Express your answer using either standard notation or scientific notation.

Answer 1

To determine how many times greater \( 1.008 \times 10^{-4} \) is than \( 4.2 \times 10^{-6} \), we can divide the two numbers:

\[ \text{Ratio} = \frac{1.008 \times 10^{-4}}{4.2 \times 10^{-6}} \]

This can be split into two parts: the coefficients and the powers of ten.

1. Divide the coefficients: \[ \frac{1.008}{4.2} = 0.24 \]

2. Subtract the exponents of 10 (using the property of exponents \( a^m \div a^n = a^{m-n} \)): \[ 10^{-4} \div 10^{-6} = 10^{-4 - (-6)} = 10^{-4 + 6} = 10^{2} \]

Now combine the results: \[ \text{Ratio} = 0.24 \times 10^{2} \] \[ = 24 \]

Thus, \( 1.008 \times 10^{-4} \) is 24 times greater than \( 4.2 \times 10^{-6} \).

In scientific notation, this can also be expressed as: \[ 2.4 \times 10^1 \]

So, the final answer is 24 or \( 2.4 \times 10^1 \).