Question

Write the appropriate symbol in the blank \((>,<,\) or \(=)\). (a) \(37.12 \mathrm{~g} \longrightarrow 0.3712 \mathrm{~kg}\) (b) \(28 \mathrm{~m}^{3} \longrightarrow 10^{2} \mathrm{~cm}^{3}\) (c) \(525 \mathrm{~mm}\) \(525 \times 10^{6} \mathrm{nm}\)

Short answer

Question: Compare the following quantities and choose the appropriate symbol (>, <, or =): a) 37.12 g and 0.3712 kg b) 28 m³ and 100 cm³ c) 525 mm and 525,000,000 nm Answer: a) 37.12 g < 0.3712 kg b) 28 m³ > 100 cm³ c) 525 mm = 525,000,000 nm

Step-by-step solution

(a) Conversion of units

First, let's convert the given mass from grams to kilograms: \(37.12 \mathrm{~g} = 37.12 \times 10^{-3} \mathrm{~kg} = 0.03712 \mathrm{~kg}\) Now, we can compare the numerical values and choose the appropriate symbol.

(a) Comparison of values

We now have: \(0.03712 \mathrm{~kg} \compare 0.3712 \mathrm{~kg}\) Since 0.03712 is less than 0.3712, we can conclude that: \(0.03712 \mathrm{~kg} < 0.3712 \mathrm{~kg}\)

(b) Conversion of units

First, let's convert the given volume from cubic meters to cubic centimeters: \(28 \mathrm{~m}^{3} = 28 \times (10^{2})^{3} \mathrm{~cm}^{3} = 28 \times 10^{6} \mathrm{~cm}^{3}\) Now, we can compare the numerical values and choose the appropriate symbol.

(b) Comparison of values

We now have: \(28 \times 10^{6} \mathrm{~cm}^{3} \compare 10^{2} \mathrm{~cm}^{3}\) Since 28 x 10^6 is greater than 10^2, we can conclude that: \(28 \times 10^{6} \mathrm{~cm}^{3} > 10^{2} \mathrm{~cm}^{3}\)

(c) Conversion of units

First, let's convert the given length from millimeters to nanometers: \(525 \mathrm{~mm} = 525 \times 10^{6} \mathrm{~nm}\) Now, we can compare the numerical values and choose the appropriate symbol.

(c) Comparison of values

We now have: \(525 \times 10^{6} \mathrm{~nm} \compare 525 \times 10^{6} \mathrm{~nm}\) Since both values are equal, we can conclude that: \(525 \times 10^{6} \mathrm{~nm} = 525 \times 10^{6} \mathrm{~nm}\)