Question

write each of the following numbers in standard form:

1. 4.8×10³
2. 9.1×10⁻⁴
3. 1.013×10²
4. 1.60×10⁻²

measurement:

1. report the measured volume from the figure, being sure to use the correct amount of significant figures and proper units.
2. when reporting a measurement in centimeters made with a meter stick that has millimeters marked, the final digit should be in the

a) ones (91 cm)
b) tenths (91.4 cm)
c) hundredreths (91.45 cm)
d) thousandths (91.450 cm)
density

1. calculate the density of an object measured to be 32 cm³ and 86.2 grams. round with proper significant figures.
2. calculate the mass of an object with a density of 1.8 g/cm³ and a volume of 1200 cm³. report your answer with significant figures, in kilograms. show factor label method.

Explanation:

Step1: Convert scientific - notation to standard form

1. For \(4.8\times10^{3}\), move the decimal point 3 places to the right. So \(4.8\times10^{3}=4800\).
2. For \(9.1\times10^{- 4}\), move the decimal point 4 places to the left. So \(9.1\times10^{-4}=0.00091\).
3. For \(1.013\times10^{2}\), move the decimal point 2 places to the right. So \(1.013\times10^{2}=101.3\).
4. For \(1.60\times10^{-2}\), move the decimal point 2 places to the left. So \(1.60\times10^{-2}=0.0160\) (keep the trailing zero for significant - figure reasons).

Step2: Read volume from graduated cylinder

Estimate the volume to one - tenth of the smallest division. The smallest division on a 25 - mL graduated cylinder is 0.5 mL. The meniscus is at 11.5 mL.

Step3: Determine significant digits for measurement

A meter - stick marked in millimeters has an uncertainty in the hundredths place when measuring in centimeters. So the final digit should be in the hundredths place. The answer is C.

Step4: Calculate density

The density formula is \(D=\frac{m}{V}\), where \(m = 86.2\ g\) and \(V = 32\ cm^{3}\). \(D=\frac{86.2\ g}{32\ cm^{3}}\approx2.7\ g/cm^{3}\) (rounded to two significant figures since 32 has two significant figures).

Step5: Calculate mass using density formula

We know \(D=\frac{m}{V}\), so \(m = D\times V\). Given \(D = 1.8\ g/cm^{3}\) and \(V=1200\ cm^{3}\), then \(m=(1.8\ g/cm^{3})\times1200\ cm^{3}=2160\ g\). Convert to kilograms: \(m = 2.16\ kg\) (three significant figures).

Answer:

1. 4800
2. 0.00091
3. 101.3
4. 0.0160
5. 11.5 mL
6. C. Hundredths (91.45 cm)
7. \(2.7\ g/cm^{3}\)
8. 2.16 kg