Question

convert 0.0064 kilogram into milligram (record answer with correct significant digits and unit)

Explanation:

Step1: Recall unit conversion factors

We know that \(1\) kilogram (\(kg\)) \( = 1000\) grams (\(g\)) and \(1\) gram (\(g\)) \( = 1000\) milligrams (\(mg\)). So, \(1\) \(kg=1000\times1000\) \(mg = 10^{6}\) \(mg\).

Step2: Convert kilograms to milligrams

To convert \(0.0064\) \(kg\) to \(mg\), we multiply by the conversion factor \(10^{6}\) \(mg/kg\).

$$0.0064\ kg\times10^{6}\ \frac{mg}{kg}=0.0064\times10^{6}\ mg$$

$$0.0064\times10^{6}=6400\ mg$$

Now, check significant digits. The number \(0.0064\) has two significant digits (the non - zero digits 6 and 4). So, we present the answer with two significant digits? Wait, no, \(0.0064\) is \(6.4\times 10^{- 3}\), when we multiply by \(10^{6}\), we get \(6.4\times10^{3}\) \(mg\) or \(6400\) \(mg\). But let's check the significant figures again. \(0.0064\) has two significant digits? Wait, no: leading zeros are not significant, so \(0.0064\) has two significant digits? Wait, \(0.0064\) is \(6.4\times10^{-3}\), so when we do the conversion:
\(0.0064\ kg = 0.0064\times1000\ g=6.4\ g\) (two significant digits), then \(6.4\ g\times1000\ mg/g = 6400\ mg\). But in terms of significant digits, \(6.4\times10^{3}\ mg\) (which is \(6400\ mg\)) has two significant digits? Wait, no, \(6.4\times10^{3}\) has two significant digits, while \(6400\) could be ambiguous, but since our original number \(0.0064\) has two significant digits, we should present the answer as \(6.4\times 10^{3}\ mg\) or \(6400\ mg\) (with the understanding that the trailing zeros are not significant, but in this case, since we have two significant digits from the original number, \(6400\) can be written as \(6.4\times10^{3}\) to show two significant digits. However, let's re - examine the original number: \(0.0064\) kilograms. The digits 6 and 4 are significant, so two significant digits. So the conversion gives \(0.0064\times10^{6}=6400\) milligrams. But if we consider significant figures, \(6.4\times 10^{3}\) milligrams (which is 6400 milligrams) is correct with two significant digits. Wait, but maybe I made a mistake in significant figures. Let's see: \(0.0064\) is \(6.4\times10^{-3}\), multiplying by \(10^{6}\) gives \(6.4\times10^{3}\), which is 6400. So the answer is \(6400\ mg\) (or \(6.4\times 10^{3}\ mg\)) with the correct unit.

Answer:

\(6400\ mg\) (or \(6.4\times 10^{3}\ mg\))