Question

1. how many significant figures are in each of the following measurements?

a) 0.4004 ml
b) 1.00030 km
c) 6000 g
d) 400. nm

1. perform the following calculations. express the answers with the correct number of significant digits.

a) 6.078 g + 0.3329 g
b) 8.2 cm - 7.11 cm
c) (0.8102 m)(3.44 m)
d) 94.20 g÷3.16722 ml

1. calculate the product of 0.002115 m and 0.0000405 m. express the answer in scientific notation and with the correct number of significant figures.
2. a sample of a certain material has a mass of 2.03×10⁻³ g. calculate the volume of the sample, given that the density is 9.133×10⁻¹ g/cm³

multiple choice

1. the unit m³ is used to express

a. length.
b. mass.
c. volume.
d. density.

1. si base units for length and mass are

a. centimeter and gram.
b. meter and gram.
c. centimeter and kilogram.
d. meter and kilogram.

1. the abbreviations for units of length in order from smallest to largest are

a. m, cm, mm, km.
b. mm, m, cm, km.
c. km, mm, cm, m.
d. mm, cm, m, km.

Explanation:

Step1: Determine significant figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros are not significant. Trailing zeros are significant only if there is a decimal point.

Step2: Analyze 0.4004 mL

There are 4 non - zero and between non - zero zeros, so 4 significant figures.

Step3: Analyze 1.00030 km

Non - zero digits and zeros between non - zero digits and trailing zero after decimal are significant, so 6 significant figures.

Step4: Analyze 6000 g

Without a decimal point, trailing zeros may not be significant, so 1 significant figure.

Step5: Analyze 400. nm

The decimal point makes the trailing zeros significant, so 3 significant figures.

Step6: Calculate 6.078 g+0.3329 g

$6.078 + 0.3329=6.4109$. For addition, round to the least number of decimal places among the numbers being added. 6.078 has 3 decimal places and 0.3329 has 4 decimal places, so round to 3 decimal places: 6.411 g.

Step7: Calculate 8.2 cm - 7.11 cm

$8.2−7.11 = 1.09$. 8.2 has 1 decimal place, so round to 1 decimal place: 1.1 cm.

Step8: Calculate (0.8102 m)(3.44 m)

$0.8102\times3.44 = 2.787088$. For multiplication, round to the least number of significant figures among the numbers being multiplied. 0.8102 has 4 significant figures and 3.44 has 3 significant figures, so round to 3 significant figures: 2.79 m².

Step9: Calculate 94.20 g÷3.16722 mL

$94.20\div3.16722\approx29.741$. 94.20 has 4 significant figures and 3.16722 has 6 significant figures, so round to 4 significant figures: 29.74 g/mL.

Step10: Calculate product of 0.002115 m and 0.0000405 m

$0.002115\times0.0000405=8.56575\times10^{-8}$. 0.002115 has 4 significant figures and 0.0000405 has 3 significant figures, so round to 3 significant figures: $8.57\times10^{-8}$ m².

Step11: Calculate volume given mass and density

The density formula is $
ho=\frac{m}{V}$, so $V = \frac{m}{
ho}$. Given $m = 2.03\times10^{-3}$ g and $
ho=9.133\times10^{-1}$ g/cm³. Then $V=\frac{2.03\times10^{-3}}{9.133\times10^{-1}}\approx2.22\times10^{-3}$ cm³.

Step12: Answer multiple - choice 14

The unit $m^{3}$ is used to express volume. So the answer is c. volume.

Step13: Answer multiple - choice 15

The SI base units for length and mass are meter and kilogram. So the answer is d. meter and kilogram.

Step14: Answer multiple - choice 16

The abbreviations for units of length from smallest to largest are mm (millimeter), cm (centimeter), m (meter), km (kilometer). So the answer is d. mm, cm, m, km.

Answer:

1. a) 4

b) 6
c) 1
d) 3

1. a) 6.411 g

b) 1.1 cm
c) 2.79 m²
d) 29.74 g/mL

1. $8.57\times10^{-8}$ m²
2. $2.22\times10^{-3}$ cm³
3. c. volume
4. d. meter and kilogram
5. d. mm, cm, m, km