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Chapter 2: Problem 197

How many significant figures are there in each number: (a) \(5.300 \times 10^{-2}\) (b) \(3.2 \times 10^{5}\) (c) \(0.00890 \times 10^{-4}\) (d) \(7.9600000 \times 10^{10}\) (e) \(8.030 \times 10^{21}\)

Short Answer

Expert verified
The numbers of significant figures for each given number are: (a) 4, (b) 2, (c) 3, (d) 8, and (e) 4.

Step by step solution

01

(a) Counting significant figures for \(5.300 \times 10^{-2}\)

The given number is \(5.300 \times 10^{-2}\). All non-zero digits are significant, and zeros between significant figures are also significant. Therefore, there are 4 significant figures in this number: \(5, 3, 0,\) and \(0\).
02

(b) Counting significant figures for \(3.2 \times 10^{5}\)

The given number is \(3.2 \times 10^{5}\). All non-zero digits are significant, and zeros between significant figures are also significant. Therefore, there are 2 significant figures in this number: \(3\) and \(2\).
03

(c) Counting significant figures for \(0.00890 \times 10^{-4}\)

The given number is \(0.00890 \times 10^{-4}\). All non-zero digits are significant, zeros between significant figures are also significant, and zeros used for spacing the decimal point are not considered significant. Therefore, there are 3 significant figures in this number: \(8, 9,\) and \(0\).
04

(d) Counting significant figures for \(7.9600000 \times 10^{10}\)

The given number is \(7.9600000 \times 10^{10}\). All non-zero digits are significant, and zeros between significant figures are also significant. In addition, zeros after a decimal point and trailing a non-zero digit are considered significant. Therefore, there are 8 significant figures in this number: \(7, 9, 6,\) and \(5\) zeros.
05

(e) Counting significant figures for \(8.030 \times 10^{21}\)

The given number is \(8.030 \times 10^{21}\). All non-zero digits are significant, and zeros between significant figures are also significant. In addition, zeros after a decimal point and trailing a non-zero digit are considered significant. Therefore, there are 4 significant figures in this number: \(8, 0, 3,\) and \(0\).

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Most popular questions from this chapter

A student takes three measurements of the mass of an object. If the actual mass is \(8.54 \mathrm{~g}\), indicate whether each set of measurements is precise but not accurate, accurate but not precise, both accurate and precise, or neither accurate nor precise: (a) \(6.38 \mathrm{~g}, 9.23 \mathrm{~g}, 4.36 \mathrm{~g}\) (b) \(8.53 \mathrm{~g}, 8.59 \mathrm{~g}, 8.55 \mathrm{~g}\) (c) \(9.53 \mathrm{~g}, 8.54 \mathrm{~g}, 7.54 \mathrm{~g}\) (d) \(6.25 \mathrm{~g}, 6.27 \mathrm{~g}, 6.26 \mathrm{~g}\)

Convert to cal \(/ \mathrm{g} \cdot{ }^{\circ} \mathrm{C}:\) (a) \(1.04 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of nitrogen gas) (b) \(0.84 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) (the specific heat of carbon dioxide gas)

Write each number in standard notation: (a) \(1.79 \times 10^{-2}\) (b) \(8.76 \times 10^{-9}\) (c) \(4.88 \times 10^{10}\) (d) \(7.52 \times 10^{1}\) (e) \(8.37 \times 10^{\circ}\) (f) \(4.184 \times 10^{4}\)

A \(2.50-g\) piece of wood is burned in a calorimeter that contains \(0.200 \mathrm{~kg}\) of water. The burning causes the water temperature to increase from \(22.1^{\circ} \mathrm{C}\) to \(28.7^{\circ} \mathrm{C}\). How much heat energy is released in joules? What is the energy content of the wood in joules per gram of wood?

Do the following calculations and express each answer in scientific notation: (a) \(\left(5.03 \times 10^{2}\right)+\left(8.1 \times 10^{1}\right)\) (b) \(\left(8.32 \times 10^{-5}\right) \times\left(0.53 \times 10^{4}\right)\) (c) \(\frac{6.02 \times 10^{23}}{3}\), where the 3 is an exact number (d) \(\left(3.960 \times 10^{3}\right)-\left(4.62 \times 10^{2}\right)\)
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