Question

convert 430 nm to cm.
430 nm → ??? cm
tap arrows to move the decimal point.
arrows and decimal grid
on a calculator, this conversion would involve ...
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Explanation:

Step1: Recall unit conversions

We know that \(1\space \text{m} = 10^{9}\space \text{nm}\) and \(1\space \text{m} = 100\space \text{cm}\). So, first convert nanometers to meters, then meters to centimeters.

Step2: Convert nm to m

To convert \(430\space \text{nm}\) to meters, use the conversion factor \(\frac{1\space \text{m}}{10^{9}\space \text{nm}}\). So, \(430\space \text{nm}=430\times\frac{1}{10^{9}}\space \text{m}=4.3\times 10^{-7}\space \text{m}\).

Step3: Convert m to cm

Now, convert meters to centimeters using the conversion factor \(\frac{100\space \text{cm}}{1\space \text{m}}\). So, \(4.3\times 10^{-7}\space \text{m}=4.3\times 10^{-7}\times100\space \text{cm}=4.3\times 10^{-5}\space \text{cm}\).

Alternatively, using decimal movement:
We know that \(1\space \text{cm}=10^{7}\space \text{nm}\) (since \(1\space \text{m} = 10^{2}\space \text{cm}\) and \(1\space \text{m}=10^{9}\space \text{nm}\), so \(1\space \text{cm}=\frac{10^{9}}{10^{2}}\space \text{nm} = 10^{7}\space \text{nm}\)). So to convert \(430\space \text{nm}\) to cm, we divide by \(10^{7}\). \(430\div10^{7}=4.3\times 10^{-5}\) (because dividing by \(10^{7}\) is moving the decimal point 7 places to the left. \(430 = 4.3\times10^{2}\), so \(4.3\times10^{2}\div10^{7}=4.3\times10^{-5}\)).

Answer:

\(4.3\times 10^{-5}\space \text{cm}\)