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Chapter 1: Problem 35

What is the number of significant figures in each of the following measured quantities? (a) \(601 \mathrm{~kg}\), (b) \(0.054 \mathrm{~s}\), (c) \(6.3050 \mathrm{~cm}\), (d) \(0.0105 \mathrm{~L}\) (e) \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\) (f) \(400 \mathrm{~g}\).

Short Answer

Expert verified
(a) 3 significant figures (b) 2 significant figures (c) 5 significant figures (d) 3 significant figures (e) 5 significant figures (f) 1 significant figure

Step by step solution

01

(a) Number of significant figures in 601 kg

Since there are no leading or trailing zeros, we simply count the number of digits. There are 3 nonzero digits (6, 0, and 1), so there are 3 significant figures.
02

(b) Number of significant figures in 0.054 s

Here, there are leading zeros (0) before the first nonzero digits, which don't count as significant figures. So there are only 2 nonzero digits (5 and 4) which are significant giving us 2 significant figures.
03

(c) Number of significant figures in 6.3050 cm

In this example, we have trailing zeros after the decimal point, which counts as significant figures. So, along with 3 nonzero digits (6, 3, and 5) we also have 2 trailing zeros after the decimal point (50). So there are 5 significant figures in this measurement.
04

(d) Number of significant figures in 0.0105 L

We don't count the leading zeros (0). There are 3 digits namely 1, 0, and 5, and we count the zero between nonzero digits as significant. So, there are 3 significant figures in this measurement.
05

(e) Number of significant figures in \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\)

In scientific notation, we only need to look at the coefficient (the number before the exponent). As there are 3 nonzero digits (7, 0, and 5) and 2 trailing zeros after the decimal point, there are 5 significant figures.
06

(f) Number of significant figures in 400 g

As there is no decimal point in this number, we do not count the trailing zeros. So, there is only 1 nonzero digit (number 4) making it 1 significant figure. To summarise: (a) 601 kg has 3 significant figures. (b) 0.054 s has 2 significant figures. (c) 6.3050 cm has 5 significant figures. (d) 0.0105 L has 3 significant figures. (e) \(7.0500 \times 10^{-3} \mathrm{~m}^{3}\) has 5 significant figures. (f) 400 g has 1 significant figure.

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Most popular questions from this chapter

A package of aluminum foil contains \(50 \mathrm{ft}^{2}\) of foil, which weighs approximately 8.0 oz. Aluminum has a density of \(2.70 \mathrm{~g} / \mathrm{cm}^{3}\). What is the approximate thickness of the foil in millimeters?

Automobile batteries contain sulfuric acid, which is commonly referred to as "battery acid." Calculate the number of grams of sulfuric acid in 1.00 gallon of battery acid if the solution has a density of \(1.28 \mathrm{~g} / \mathrm{mL}\) and is \(38.1 \%\) sulfuric acid by mass.

(a) What is the difference between a hypothesis and a theory? (b) Explain the difference between a theory and a scientific law. Which addresses how matter behaves, and which addresses why it behaves that way?

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