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Chapter 1: Problem 45

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

Short Answer

Expert verified
(a) 3 significant figures (b) 2 significant figures (c) 5 significant figures (d) 3 significant figures (e) 4 significant figures (f) 1 significant figure

Step by step solution

01

(a) 601 kg

This quantity contains non-zero digits only, so all of them are significant. Hence, there are \(\boxed{3}\) significant figures in 601 kg.
02

(b) 0.054 s

Leading zeroes are not significant, so we will ignore 0 before the decimal point. Now, we have two non-zero digits (5 and 4), both of them are significant. The number of significant figures in 0.054 s is \(\boxed{2}\).
03

(c) 6.3050 cm

This quantity has one non-zero digit before the decimal point and four digits after the decimal point. The trailing zero (the last zero) is considered significant because it's after the decimal point. So, there are \(\boxed{5}\) significant figures in 6.3050 cm.
04

(d) 0.0105 L

In this case, leading zeros (0 before the decimal point and 0 after the decimal point) are not significant. Then, we have three digits, where one zero in between significant digits (1 and 5). So, there are \(\boxed{3}\) significant figures in 0.0105 L.
05

(e) 7.0500 x 10^{-3} m^3

Here we have all non-zero digits (7, 5) and two trailing zeroes after the decimal point (zeros are significant because they are after the decimal point). The digit in the exponent of 10 (-3) doesn't count towards the significant figures. So, there are \(\boxed{4}\) significant figures in 7.0500 x 10^{-3} m^3.
06

(f) 400 g

This quantity contains one non-zero digit (4) and two trailing zeroes. However, since there is no decimal point, the trailing zeroes are not significant. Therefore, there is only \(\boxed{1}\) significant figure in 400 g.

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Most popular questions from this chapter

Indicate the number of significant figures in each of the following measured quantities: (a) \(3.774 \mathrm{km},\) (b) 205 \(\mathrm{m}^{2}\) , (c) \(1.700 \mathrm{cm},(\mathbf{d}) 350.00 \mathrm{K},(\mathbf{e}) 307.080 \mathrm{g},(\mathbf{f}) 1.3 \times 10^{3} \mathrm{m} / \mathrm{s}\) .

(a) Calculate the kinetic energy, in joules of a 1200 -kg automobile moving at 18 \(\mathrm{m} / \mathrm{s}\) . ( b ) Convert this energy to calories.(c) When the automobile brakes to a stop is the "lost" kinetic energy converted mostly to heat or to some form of potential energy?

Which separation method is better suited for separating a solution of sugar and water into pure substances, filtration or distillation?

A 25.0 -cm-long cylindrical glass tube, sealed at one end, is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 45.23 g. The density of ethanol is 0.789 \(\mathrm{g} / \mathrm{mL}\) . Calculate the inner diameter of the tube in centimeters.

The total rate at which power is used by humans world wide is approximately 15 TW (terawatts). The solar flux averaged over the sunlit half of Earth is 680 \(\mathrm{W} / \mathrm{m}^{2}\) (assuming no clouds). The area of Earth's disc as seen from the Sun is \(1.28 \times 10^{14} \mathrm{m}^{2} .\) The surface area of Earth is approximately \(197,000,000\) square miles. How much of Earth's surface would we need to cover with solar energy collectors to power the planet for use by all humans? Assume that the solar energy collectors can convert only 10\(\%\) of the available sun light into useful power.
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