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Chapter 1: Problem 31

Convert the following expressions into exponential notation: (a) 3 terameters \((\mathrm{tm})\) (b) 2.5 femtoseconds (fs) (c) 57 micrometers \((\mu m)\) (d) 8.3 megagrams (mg).

Short Answer

Expert verified
(a) 3 Terameters (Tm) = \(3 \times 10^{12}\) meters (m) (b) 2.5 Femtoseconds (fs) = \(2.5 \times 10^{-15}\) seconds (s) (c) 57 Micrometers (μm) = \(57 \times 10^{-6}\) meters (m) (d) 8.3 Megagrams (Mg) = \(8.3 \times 10^{6}\) grams (g)

Step by step solution

01

Understating the prefixes

The given prefixes have the following exponential values: - Tera (T) means 10^12 - Femto (f) means 10^(-15) - Micro (μ) means 10^(-6) - Mega (M) means 10^6 Now, we will convert the quantities.
02

(a) Converting 3 terameters to exponential notation

As Tera (T) means 10^12, we can replace the T with the exponential notation: 3 Terameters (Tm) = \(3 \times 10^{12}\) meters (m)
03

(b) Converting 2.5 femtoseconds to exponential notation

As Femto (f) means 10^(-15), we can replace the f with the exponential notation: 2.5 Femtoseconds (fs) = \(2.5 \times 10^{-15}\) seconds (s)
04

(c) Converting 57 micrometers to exponential notation

As Micro (μ) means 10^(-6), we can replace the μ with the exponential notation: 57 Micrometers (μm) = \(57 \times 10^{-6}\) meters (m)
05

(d) Converting 8.3 megagrams to exponential notation

As Mega (M) means 10^6, we can replace the M with the exponential notation: 8.3 Megagrams (Mg) = \(8.3 \times 10^{6}\) grams (g)

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