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(I) The Sun, on average, is 93 million miles from Earth. How many meters is this? Express $(a) \quad$ using powers of ten, and $(b)$ using a metric prefix.

A) $1.5 \times 10^{11} m$B) $1.5 \times 10^{11} m=150$ gigameters $=0.15$ terameters

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

Brad S.

September 21, 2020

Why did they use the term metric prefix?

Sarah H.

It's a wonderful question you had Brad, basically metric prefix is a unit prefix that precedes a basic unit of measure to indicate a multiple or sub-multiple of the unit.

Eric V.

How to use powers of ten?

Julia M.

So the answer for that Eric. In powers of ten notation, large numbers are written using ten to a power, or exponent. The exponent tells you how many times ten is to be multiplied by itself to equal the number you wish to write. For example, 100 can be wri

Doug F.

September 22, 2020

Anyone else confused by the gigameters and terameters, can someone explain?

Erica G.

Hey Doug! Basically gigameter (Gm) is a decimal multiple of the base metric (SI) measurement unit of length, the meter. The SI prefix Giga stands for billion. The Gigameter (Gm) is equal to 1,000,000,000 meters while a terameter (Tm) is a decimal multiple

Jundel N.

October 6, 2020

Catherine A.

October 26, 2020

Zachary W., thanks this was super helpful.

David Base G.

That was not easy, glad this was able to help

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Washington

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Okay, an hour question. We are told that the son is, on average 93,000,000 miles away from the earth. And it wants to know how far is this if expressed in meters and wants us through this expressive expression in meters in two different ways that wants us to a do it using powers of 10 and b using the metric prefixes which we got from table four and the book. Okay, so we're given that our distance, which I live, Blaise de, is 93,000,000 miles, which can be written as 93 times 10 to the six miles. So then the question is, what is the distance and meters? Okay, so the first thing we want to know is the conversion between miles and meters. So if we look this up, we find that one mile right This outgoing mile is equal to 1,609 0.34 meters on the abbreviation for meters is just him. Sole right. Just, um Okay, so now we can use this conversion to convert our 93 times 10 to the six miles for the average distance of the earth from the sun and the meters. So we have our 93,000 earned 93 times, 10 to the six miles. Well, Clyde, out by our conversion, which is 1,600 on nine. Clean 34 meters for every mile. That's per one mile. Okay, that's more like it. Him, All right. And if you go ahead and plug this in their calculator, you get that. This is well, not exactly. We'll use approximations. This is approximately 1.5 times 10 of the 11 meters. Okay, so we've expressed that in powers attempt, okay? And the reason we wrote it as ah 1.5. Using these two significant figures is because we were given 93 times 10 to the six miles or 93,000,000 miles, which has two significant figures. So we'll stick to the two significant figures. Okay, so now for part B, we need to re convert this 1.5 times 10 of the 11 meters. Um sorry, not convert, but expressed this 1.5 times 10 to the 11 meters in terms of the prefix is that we were given in our table. So one of the prefixes is giga. So Giga is 10 to the nine. So we can write this 1.5 times 10 to the 11 meters. We can rewrite this as 150 just by moving the decimal place 150 times 10 to the nine meters. Okay. And as I just stated, tend to the nine is equivalent to Giga so we can write this as 150 giga meters. Now the ah shorthand for giga is just capital G. So we can just right capital G m for Giga meters. Okay, there's your solution for party.

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