Determine which of the values could be used to clear decimals in the given equation. \( 0.001-0.005 x=0.4 x \) \( \square 10,000 \)

To clear the decimals in the equation \( 0.001 - 0.005x = 0.4x \), we can multiply the entire equation by a power of 10 that will eliminate all the decimal places. The largest decimal in the equation is \( 0.4 \), which has one decimal place. The other decimals, \( 0.001 \) and \( 0.005 \), have three and two decimal places, respectively. To eliminate all decimals, we should multiply by \( 10^3 = 1000 \), since this will shift all decimal points three places to the right. Let's multiply the entire equation by \( 1000 \): \[ 1000(0.001) - 1000(0.005x) = 1000(0.4x) \] This simplifies to: \[ 1 - 5x = 400x \] Now, the equation is free of decimals. Thus, the value that could be used to clear the decimals in the equation is \( 1000 \). Since the problem mentions \( \square 10,000 \), we can also consider \( 10,000 \) as a possible multiplier. If we multiply the original equation by \( 10,000 \): \[ 10,000(0.001) - 10,000(0.005x) = 10,000(0.4x) \] This simplifies to: \[ 10 - 50x = 4000x \] This also clears the decimals, so \( 10,000 \) can indeed be used to clear the decimals. In conclusion, both \( 1000 \) and \( 10,000 \) can be used to clear the decimals in the equation. However, since the problem specifically asks about \( \square 10,000 \), the answer is: \[ \text{Yes, } 10,000 \text{ can be used to clear the decimals.} \]