Given these measurements, identify the number of significant figures and rewrite in scientific notation. (a) \(0.00574 \mathrm{kg}\) (b) \(2 \mathrm{m}\) (c) \(0.450 \times 10^{-2} \mathrm{m}\) (d) \(45.0 \mathrm{kg}\) (e) \(10.09 \times 10^{4} \mathrm{s}\) (f) \(0.09500 \times 10^{5} \mathrm{mL}\)

Short Answer

Expert verified
Question: Rewrite each of the following measurements in scientific notation and identify the number of significant figures: a) 0.00574 kg b) 2 m c) \(0.450 \times 10^{-2}\ m\) d) 45.0 kg e) \(10.09 \times 10^4\ \mathrm{s}\) f) \(0.09500 \times 10^5\ \mathrm{mL}\) Answer: a) 0.00574 kg = \(5.74 \times 10^{-3}\ kg\), 3 significant figures b) 2 m = \(2 \times 10^0\ m\), 1 significant figure c) \(0.450 \times 10^{-2}\ m\) = \(0.450 \times 10^{-2}\ m\), 3 significant figures d) 45.0 kg = \(4.50 \times 10^1\ kg\), 3 significant figures e) \(10.09 \times 10^4\ \mathrm{s}\) = \(10.09 \times 10^4\ \mathrm{s}\), 4 significant figures f) \(0.09500 \times 10^5\ \mathrm{mL}\) = \(9.500 \times 10^4\ \mathrm{mL}\), 4 significant figures

Step by step solution

01

(a) Identify the significant figures of 0.00574 kg

For 0.00574 kg, the first three zeros are not significant, and the digits 574 are significant. Therefore, there are 3 significant figures in 0.00574.
02

(a) Rewrite 0.00574 kg in scientific notation

To rewrite 0.00574 kg in scientific notation, move the decimal point 3 places to the right: $$0.00574\ kg = 5.74 \times 10^{-3}\ kg$$.
03

(b) Identify the significant figures of 2 m

In whole numbers like 2 m, there is only 1 significant figure.
04

(b) Rewrite 2 m in scientific notation

To rewrite 2 m in scientific notation: $$2\ m = 2 \times 10^0\ m$$.
05

(c) Identify the significant figures of \(0.450 \times 10^{-2}\ m\)

In \(0.450 \times 10^{-2}\ m\), there are 3 significant figures (the digits 450).
06

(c) Rewrite \(0.450 \times 10^{-2}\ m\) in scientific notation

\(0.450 \times 10^{-2}\ m\) is already in scientific notation.
07

(d) Identify the significant figures of 45.0 kg

For 45.0 kg, the digits 45 and the zero after the decimal point are significant. There are 3 significant figures.
08

(d) Rewrite 45.0 kg in scientific notation

To rewrite 45.0 kg in scientific notation: $$45.0\ kg = 4.50 \times 10^1\ kg$$.
09

(e) Identify the significant figures of \(10.09 \times 10^4\ \mathrm{s}\)

In \(10.09 \times 10^4\ \mathrm{s}\), there are 4 significant figures (the digits 1009).
10

(e) Rewrite \(10.09 \times 10^4\ \mathrm{s}\) in scientific notation

\(10.09 \times 10^4\ \mathrm{s}\) is already in scientific notation.
11

(f) Identify the significant figures of \(0.09500 \times 10^5\ \mathrm{mL}\)

In \(0.09500 \times 10^5\ \mathrm{mL}\), there are 4 significant figures (the digits 9500).
12

(f) Rewrite \(0.09500 \times 10^5\ \mathrm{mL}\) in scientific notation

To rewrite \(0.09500 \times 10^5\ \mathrm{mL}\) in scientific notation, move the decimal point 1 place to the right: $$0.09500 \times 10^5\ \mathrm{mL} = 9.500 \times 10^4\ \mathrm{mL}$$.

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