Question

1. the diameter of a carbon atom is 0.000 000 000 154 m. what is this number expressed in scientific notation?

a. 1.54×10¹¹ m
b. 1.54×10⁻¹¹ m
c. 1.54×10¹⁰ m
d. 1.54×10⁻¹⁰ m

1. what is the boiling point of water in kelvin?

a. 0 k
b. 100 k
c. 273 k
d. 373 k

1. which of these statements about units of measurement is not true?

a. there are seven base si units and all other units are derived from these base units.
b. a measurement should have a unit preceded by a number.
c. measurements can be compared without knowing their units.
d. the choice of unit depends on the useful context of the property being measured.

1. choose the measurement which matches the liquid level in the graduated - cylinder recorded to its correct precision.
2. the density of pure diamond is 3.50 g/cm³. the diamond is placed in a graduated cylinder with water and the volume is measured to be 24.2 ml. the volume of water before adding the diamond was 23.0. what is the mass of this diamond?

a. 2.92 g
b. 4.2 g
c. 80.5 g
d. 84.7 g

1. a wavelength of visible violet light measures 380 nm. this measurement in scientific notation is

a. 3.80 nm
b. 380×10⁻⁹ m
c. 3.80×10⁻⁹ m
d. 3.80×10⁻⁷ m
e. 3.8×10⁻⁷ m

1. the length of the pencil is most precisely recorded in cm as

Explanation:

Step1: Convert carbon - atom diameter to scientific notation

The number is 0.000000000154 m. Move the decimal point 10 places to the right to get a number between 1 and 10. So, it is $1.54\times10^{- 10}$ m.

Step2: Find boiling point of water in Kelvin

The boiling point of water in Celsius is 100°C. Using the conversion formula $K = ^{\circ}C+273$, we have $K=100 + 273=373$ K.

Step3: Analyze measurement - unit statement

Measurements cannot be compared without knowing their units. For example, 5 meters and 5 kilograms are not comparable without units. So, statement c is not true.

Step4: Read liquid level in graduated cylinder

The graduated - cylinder has markings every 1 mL. The liquid level is between 19 mL and 20 mL. Reading to one decimal place for an instrument with 1 - mL intervals, the reading is 19.0 mL.

Step5: Calculate mass of diamond

The volume of the diamond $V=24.2 - 23.0=1.2$ mL. Since 1 mL = 1 $cm^{3}$, $V = 1.2$ $cm^{3}$. Using the density formula $
ho=\frac{m}{V}$, we can solve for $m$. Given $
ho = 3.50$ g/$cm^{3}$, then $m=
ho V=3.50\times1.2 = 4.2$ g.

Step6: Convert wavelength to scientific notation

Since 1 nm=$10^{-9}$ m, 380 nm = $380\times10^{-9}$ m. In proper scientific notation, $380\times10^{-9}=3.80\times10^{2}\times10^{-9}=3.80\times10^{-7}$ m.

Step7: Record pencil length precisely

The ruler has markings every 1 mm. Reading to one decimal place, the length of the pencil is 7.5 cm.

Answer:

1. c. $1.54\times 10^{-10}$ m
2. d. 373 K
3. c. Measurements can be compared without knowing their units.
4. c. 19.0 mL
5. b. 4.2 g
6. d. $3.80\times 10^{-7}$ m
7. a. 7.5 cm