Question

scientific notation makes large numbers easier to write. it also provides you with quick information about the sizes of the numbers. for example, pluto and haumea are both dwarf planets. pluto has a mass of 1.305×10^22 kilograms, and haumea has a mass of 4.006×10^21 kilograms. without rewriting the mass of each planet, can you tell which of these dwarf planets is larger? explain your reasoning.

Explanation:

Step1: Compare the exponents of scientific - notation

When comparing numbers in scientific notation \(a\times10^{n}\), if the exponents \(n\) are different, the number with the larger exponent is larger. The mass of Pluto is \(1.305\times 10^{-22}\) kg and the mass of Haumea is \(4.006\times 10^{-21}\) kg. The exponent of \(10\) for Pluto is \(- 22\) and for Haumea is \(-21\). Since \(-21>-22\).

Step2: Conclusion

Haumea has a larger mass because the exponent of \(10\) in its scientific - notation representation is greater than that of Pluto.

Answer:

Haumea is larger because the exponent of \(10\) in its mass's scientific - notation (\(-21\)) is greater than the exponent of \(10\) in Pluto's mass's scientific - notation (\(-22\)).