Question

I need help with this plz.

The length of a city block running north to south in New York City is about 5 X 10^-2 miles. The distance from New York City to Mumbai, India, is about 7.5 X10^3 miles. The distance from New York City to Mumbai is about how many times the length of a New York City north-south block?

Show your work.

Answer 1

15×10^4

Explanation:

Length of New York City =
`5* 10^-^2\: miles`

The distance from New York City to Mumbai, India =
`7.5* 10^3`

The distance from New York City to Mumbai is about how many times the length of a New York City north-south block? can be translated into the equation :

`5 * 10^-^2 * x=7.5 * 10^3\\`

To solve the equation ,

`5* \:10^(-2)x=7.5* \:10^3\\\\10^3=1000\\\\5* \:10^(-2)x=1000* \:7.5\\\\\mathrm{Multiply\:the\:numbers:}\:7.5* \:1000=7500\\\\5* \:10^(-2)x=7500\\\\Simplify\:5* \:10^(-2) :\:(1)/(20) \\\\(1)/(20)x=7500\\\\\mathrm{Multiply\:both\:sides\:by\:}20\\\\20* (1)/(20)x=7500* \:20\\\\Simplify\\\\x=150000\\\\x = 15* 10^4`

Answer 2

so nyc=5 times 10^-2 miles

NYC-Mumbai=7.5 times 10^3

so

5 times 10^-2 times x=7.5 times 10^3

divide both sdies by 5 times 10^-2

x=(7.5 times 10^3)/(5 times 10^-2)

when dividing scientific notation you do this

x=(7.5 times 10^3)/(5 times 10^-2)=(7.5/5) times ((10^3)/(10^-2))

to divide exponents just subtract top from bottom

3-(-2)=5

answer is

x=1.5 times 10^5