Convert the following expressions into exponential notation: (a) 3 terameters (tm) (b) 2.5 femto

Convert the following expressions into exponential notation:...

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Key Concepts

Exponential Notation

Exponential notation, often referred to as scientific notation, is a method of writing numbers as a product of a coefficient and a power of ten. This format is especially useful for representing very large or very small numbers clearly and concisely, and it is commonly used in scientific and engineering calculations.

SI Prefixes

SI prefixes are standardized multipliers that indicate powers of ten to simplify the representation of quantities. They allow for easy conversion between different scales by associating specific prefixes (such as tera, femto, micro, and mega) with corresponding exponents (10^12, 10^-15, 10^-6, and 10^6 respectively), making it straightforward to express physical quantities in exponential form.

Scientific Notation Conversion

Scientific notation conversion involves the process of rewriting standard numerical expressions by incorporating the appropriate SI prefix multipliers as powers of ten. This method is essential for ensuring consistency and clarity in scientific communication, as it standardizes the representation of measurement units and facilitates calculations involving extremely large or small values.

Transcript

00:01 If we want to convert these values into exponential notation, okay, it's important that we recognize these prefixes and understand what they mean or what they indicate.

00:14 Okay, so let's start with three terameters.

00:17 So our standard unit, our standard unit for meters is just meters.

00:25 So we want to get that to just meters.

00:28 We have terameters.

00:29 So if we see terra, we know terra means 10 to the 12 power.

00:43 Okay, so if we see terameters, we know it's 10 to the 12 meters, and we have three.

00:51 So we do three times 10 to the 12th.

00:57 And that will be our meters.

00:59 Another way to do this, just to make sure you're right, would be to write out the number, three, four, okay, and then we put our decimal place in and count one, two, three, four, five, six, seven, eight, nine, ten, eleven, oh, i need another zero.

01:22 Okay, we count our decimal places.

01:24 This should be 12.

01:26 Now moving to femtose seconds, okay? when we see femto, we think 10 to the negative 15th.

01:40 Okay, 10 to the negative 15th.

01:42 So we already have a decimal place.

01:43 So we already have a decimal place.

01:43 Here.

01:46 We already have a decimal place, okay, but we want it just to be in seconds because our unit, our standard unit is seconds...