practice\n1. in the year 2013 the population of california was about 38,332,521 people. write the estimated…

practice\n1. in the year 2013 the population of california was about 38,332,521 people. write the estimated population as a single digit times a power of 10.\n2. the wavelength of green light is about 0.00000051 meter. what is this estimated wavelength as a single digit times a power of 10?\n3. the land area of connecticut is about 12,549,000,000 square meters. the land area of rhode island is about 2,707,000,000 square meters. how many times greater is the land area of connecticut than the land area of rhode island?

practice\n1. in the year 2013 the population of california was about 38,332,521 people. write the estimated population as a single digit times a power of 10.\n2. the wavelength of green light is about 0.00000051 meter. what is this estimated wavelength as a single digit times a power of 10?\n3. the land area of connecticut is about 12,549,000,000 square meters. the land area of rhode island is about 2,707,000,000 square meters. how many times greater is the land area of connecticut than the land area of rhode island?

Answer

Explanation:

Step1: Convert 38332521 to scientific - notation

Move the decimal point 7 places to the left to get a number between 1 and 10. So, $38332521 = 3.8332521\times10^{7}\approx4\times10^{7}$.

Step2: Convert 0.000000051 to scientific - notation

Move the decimal point 8 places to the right to get a number between 1 and 10. So, $0.000000051 = 5.1\times10^{-8}\approx5\times10^{-8}$.

Step3: Calculate the ratio of the land - areas

$\frac{12549000000}{2707000000}=\frac{1.2549\times10^{10}}{2.707\times10^{9}}$. Using the rule $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $\frac{1.2549}{2.707}\times10^{10 - 9}\approx0.4636\times10^{1}\approx5$.

Answer:

  1. $4\times10^{7}$
  2. $5\times10^{-8}$
  3. 5