The average distance from the sun to the planet mercury is about 58.000.000 km. the diameter of ahuman hair is about 0.0025 cm.(a) what is the distance from the sun to mercury written in scientific notation? (b) what is the diameter of a human hair written in scientific notation? (c) in comparing the measurements in parts (a) and (b), what else must be done before a comparison ismade?

To write this number in scientific notation we need to figure out how many spaces to move the decimal point to the left until we have only one digit to the left of the decimal point. Each space we move the decimal is one power of ten. So to obtain the number 2.38793387 we needed to move the decimal 5 times, or 5 powers of 10. This number to 3 significant digits is 2.39. We round the third digit up or down accordingly. So finally, the answer is:

2.39 x 105

Write the number 5.765 x 10-7 as a normal string of digits.

In the first problem you can see that multiplying by a positive power of ten indicates how many decimal places to the right one must move the decimal point to obtain a normal string of digits (we went to the left to get the scientific notation, it's opposite the direction to go to obtain the normal string). So multiplying by a negative power of ten moves the decimal to the left by that power. And so we have

0.0000005765

What is (6 x 104)/(3 x 10-6)? Do not use a calculator. Show your work. What's the name of this number (i.e., how many million, billion, trillion, etc. is this)?

First off 6/3 = 2. That's easy enough. So now we are left with 104/10-6. Use the rules of multiplication and division of exponents. When dividing you subtract the exponents. So 4 - (-6) = 4 + 6 = 10. Thus the answer is

2 x 1010

or 20 x 109 = 20 Billion

A light-year is the distance light travels in one year. If light travels at a speed of 186,000 miles/second how many miles are there in a light-year? How many meters is this? Give all answers in scientific notation and show all work.

Let us remember the relationship between speed, distance, and time.

distance = speed x time       (1)

In this problem we want to know the distance. We know the speed, and the time is 1 year. But the speed is not given in years, so we need to convert it into seconds. How many seconds are there in one year?

60 seconds/minute x 60 minutes/hour x 24 hours/day x 365.26 days/year = 3.16 x 107 seconds/year

So now we plug this value into equation (1) with the speed of light given

distance = (1.86 x 105 miles/second) x (3.16 x 107 seconds) = 5.88 x 1012 miles = 5.88 Trillion miles

Now, to find out how many meters this is we need only do some unit conversions. From page 544 in the text you find that 1 km = 0.6214 miles and you know that there are 103 m/km. So we have

(5.88 x 1012 miles) x (1 km/0.6214 miles) x (103 m/km) = 9.46 x 1015 m = 9.46 Quadrillion meters

Step-by-step explanation:

y < -3

step-by-step explanation:

-3y - 2 > 7

-3y -2 + 2 > 7+2

-3y > 9

-3y/-3 < 9/-3   (change the inequality sign when multiplying or dividing by a negative number)

y < -3