Dina computed the mass of 1,000 protons in grams. The calculator displayed the number 1.67E−21

. What is the mass of 1,000 protons in scientific notation?

1 answer

To find the mass of 1,000 protons in scientific notation, we first note that the mass displayed is \( 1.67 \times 10^{-21} \) grams. This represents the total mass of 1,000 protons.

To convert this to scientific notation, we need to express it in terms of the mass of a single proton. The mass of one proton is approximately \( 1.67 \times 10^{-27} \) grams. The mass of 1,000 protons can be calculated as follows:

\[ 1000 \text{ protons} = 1000 \times (1.67 \times 10^{-27}) \text{ grams} \]

Calculating this, we first write 1000 in scientific notation:

\[ 1000 = 10^3 \]

So we can combine it:

\[ 1000 \times (1.67 \times 10^{-27}) = 1.67 \times 10^3 \times 10^{-27} \]

Next, we add the exponents:

\[ 1.67 \times 10^{3 - 27} = 1.67 \times 10^{-24} \]

Thus, the mass of 1,000 protons in scientific notation is:

\[ \boxed{1.67 \times 10^{-24}} \text{ grams} \]