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 (for example 20 = 2x10 = 2x101). So to obtain the number 2.32898232 we needed to move the decimal 5 times, or 5 powers of 10. This number to 3 significant digits is 2.33. We round the third digit up or down accordingly. So finally, the answer is:
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
First off 6/3 = 2. That's easy enough. So now we are left with 10274/10268. Use the rules of multiplication and division of exponents. When dividing you subtract the exponents. So 274 - 268 = 6. Thus the answer is
If they live 3 bicycle-days away, the distance to your parents is the distance that a bicycle messenger can travel in 3 Pongian days. In one Pongian day, or 10 hours, a bicycle travelling 60 km/hr can travel 60 km/hr x 10 hr = 600 km. So in 3 Pongian days, it can travel 3x600=1800 km. So 3 bicycle-days is a distance of 1800 km. (One bicycle-day is a distance of 600 km).
Since the only means of communication is by bicycle, the time until you get the news is (assuming a bicycle was dispatched immediately and you were at home to meet it when it arrived) the time it takes a bicycle to travel the distance to your home. They live 3 bicycle-days away, so it takes 3 days for a bicycle to reach you. (The long way to do this question is to take distance d=1800 km and time t=d/speed so t = 1800 km / 60 km/hr = 30 hours = 3 days of 10 hours each).
A bicycle-year is the distance a bicycle can travel in 1 Pongian year. There are 100 days in a Pongian year, and 10 hours per Pongian day, so there are 1000 hours in a Pongian year. A bicycle can travel 60 km/hr, so in a year it can go 60 km/hr x 1000 hr = 60 000 km = 6x104 km.
The distance to Quong is 6x1011 m, but there are 1000m = 103m in a km, so the distance to Quong is 6x1011-3 = 6x108 km. There are 6x104 km in a bicycle-year (since there are 1000 hr/year, and a bicycle can travel 60 km/h), so the distance to Quong in bicycle-years is:
6x108km / 6x104km/bicycle-year = 108-4= 104.Quong is 10 000 bicycle-years away!
Since Quong is 10 000 bicycle-years away, even if the news was sent immediately, you will not get it for 10 000 Pongian years (the speed of communication is still that of a bicycle). The child will by then be 10 000 years old. Or dead, depending on the life span of Pongians, which none of us knows!
Note that in our solar system, Jupiter is over 30 light-minutes from Earth, so even with a MUCH faster speed of communication, there is a significant lag! Since the nearest stars are several light-years away, interstellar communication and travel are impractical without faster-than-light technology (which violates physics as we understand it).
Our solar system is made up of the Sun (the nearest star), and bodies (like the planets) which are gravitationally bound to it. It is much smaller than the distance to the nearest star. Our galaxy is filled with many stars (~100 billion) and their planets, as well as gas and dust. The universe is the cosmos, which is everything there is. It includes billions of galaxies.
People in other cultures on earth will still see the Big Dipper, as long as they live far enough north for it to be above the horizon, because the pattern of stars is the same from all over Earth. People on planets circling a very nearby star might see the same pattern of stars if their star were very close to us compared to the stars of the Big Dipper. But the stars making up the Big Dipper will not appear in the same pattern from the viewpoint of very distant stars. For example, if you were on a planet circling one of the stars in the Big Dipper, you clearly wouldn't see this asterism as we do!
For specificity, the stars making up the Big Dipper are between 68 and 210 light years away (see Ask A Scientist Astronomy Archive for the distances of each star), and the very nearest star is over 4 light years away, so civilizations on planets circling most other stars will not see the same pattern from the Big Dipper stars. They may well see the same stars, but they won't look like a Dipper.
The north celestial pole is the projection into space of the Earth's north pole. If I'm on the equator, then the north celestial pole is a point in space beyond my northern horizon. If you don't get this, stick a skewer in an orange. The direction that the skewer points is the north celestial pole. Now imagine yourself on the equator, and figure out which direction the skewer is pointing.
If you're standing at the South Pole, then the South Celestial Pole lies directly overhead.
Imagine you're on the earth surrounded by a giant clear sphere. As the earth rotates about the axis going through the north and south poles, the celestial sphere appears to rotate in the opposite direction about the same axis. This means the stars move in circles around the celestial poles (see the diagram here).
Since the South Celestial Pole is directly overhead, and the stars move in circles about this point, the stars are moving parallel to the horizon. They never rise or set.
If you're at the equator looking South, then East is on your left. The stars rise East (left) of the southern point on the horizon (and set west). Since the stars move in circles about the SCP, which lies on your southern horizon, you can see HALF-circles (the other half is below your horizon). Therefore the stars rise straight up from the horizon.
You would see stars setting straight down into the horizon.
Based on experience, I expect that the book will hit the floor first, and the paper will drift to the floor more slowly.
Newton's theory of gravity predicts that they will hit the floor at the same time (see the description above).
The book hit the floor with a thud. The paper drifted to the floor more slowly, and hit later.
The results of the test match the prediction I made based on my everyday experience. They did not match the predictions of Newton's theory of gravity.
The experiment doesn't take into account the effects of the air. The paper, being lighter, is more affected by the air resistance than the book. To modify the experiment, place the paper on top of the book, and then drop them. The paper never leaves the book.
Design a scientific test of astrology. In other words, design an experiment whose results will either support the assertions of astrology, or conflict with them.
I will not go into detail here, but Lab Assignment #1 contains one possible experiment, as well as a brief description of a second experiment. There are many others! One other possibility is to have your subjects write down a description of their day, then yourself compare their description with their horoscope. Another which has been done is to ask astrologers to match personality profiles with astrological signs. We'll discuss this more after you've done the lab assignment.
Here I'm hoping that you'd consider possible biases and other sources of error, and that you'd compare your results with those you'd expect based on random chance.
This is a personal opinion! See if it changes after you've done Lab Assignment #1.
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