(I) The Sun, on average, is 93 million miles from Earth. How many meters is this? Express (a)

(I) The Sun, on average, is 93 million miles from Earth. How...

Key Concepts

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one unit to another unit using conversion factors. This is crucial in mathematics and science to ensure consistency and accuracy in measurements when working with different measurement systems.

Scientific Notation

Scientific notation is a method of writing very large or very small numbers as a product of a coefficient and a power of ten. This format simplifies calculations, improves readability, and helps in accurately handling numbers in fields such as physics and engineering.

Metric Prefixes

Metric prefixes are used in the International System of Units (SI) to represent multiples or submultiples of base units in a clear and standardized way. These prefixes, such as mega-, kilo-, and milli-, allow for a compact representation of measurements across a wide range of magnitudes.

Transcript

00:01 Okay.

00:02 In our question, we are told that the sun is on average 93 million miles away from the earth.

00:09 And it wants to know how far is this if expressed in meters? and it wants us to do this expression in meters in two different ways.

00:16 It wants us to, a, do it using powers of 10, and b, using the metric prefixes, which we got from table 4 in the book.

00:26 Okay.

00:27 So we're given that our distance, which i label as d, is 93 million miles.

00:31 Which can be written as 93 times 10 to the 6 miles.

00:36 So then the question is, what is the distance in meters? so the first thing we want to know is the conversion between miles and meters.

00:44 So if we look this up, we find that one mile, write this out, one mile is equal to 1 ,609 .34 meters.

01:05 And the abbreviation for meters is just m.

01:07 So we'll write just m.

01:08 Okay, so now we can use this conversion to convert our 93 times 10 to the 6 miles for the average distance of the earth from the sun into meters.

01:23 So we have our 93 times 10 to the 6 miles.

01:28 Multiply that by our conversion, which is 1 ,609 .34 meters for every mile.

01:44 That's per one mile.

01:53 Let's look more like you now.

01:55 All right.

01:56 And if you go ahead and plug this in your calculator, you get that this is, well, not exactly.

02:00 We'll use approximations...