Question

the mass of an electron is approximately $9.1 \times 10^{-31}$ kilograms. the mass of a proton is approximately $1.7 \times 10^{-27}$ kilograms. approximately how many times greater is the mass of a proton than the mass of an electron?
1,900
55,000

Explanation:

Step1: Set up division equation

To find how many times greater the proton's mass is, divide the proton mass by the electron mass:
$$\frac{1.7 \times 10^{-27}}{9.1 \times 10^{-31}}$$

Step2: Split into coefficient and exponent parts

Separate the coefficients and powers of 10:
$$\frac{1.7}{9.1} \times \frac{10^{-27}}{10^{-31}}$$

Step3: Calculate coefficient division

Compute the coefficient ratio:
$$\frac{1.7}{9.1} \approx 0.1868$$

Step4: Simplify exponent division

Use exponent rule $10^a/10^b=10^{a-b}$:
$$10^{-27 - (-31)} = 10^{4} = 10000$$

Step5: Multiply results

Combine the two parts:
$$0.1868 \times 10000 = 1868 \approx 1900$$

Answer:

1,900