Q1. Write 0.0000204 in scientific notation.

Background

Topic: Scientific Notation

This question tests your ability to express very small numbers in scientific notation, which is a standard way of writing numbers that are too large or too small to be conveniently written in decimal form.

Key Terms and Formula:

• Scientific Notation: A number is written as , where and is an integer.

Step-by-Step Guidance

1. Identify the first nonzero digit in the number (in this case, 2).

2. Count how many places you move the decimal point to get a number between 1 and 10.

3. Write the number as a product of this new number and $10$ raised to the negative power equal to the number of decimal places moved.

Try solving on your own before revealing the answer!

Q2. Which of the following measured numbers has three significant figures?

Background

Topic: Significant Figures

This question tests your understanding of how to count significant figures in measured numbers, which is important for reporting scientific data accurately.

Key Terms:

• Significant Figures: The digits in a measurement that are known with certainty plus one estimated digit.

Step-by-Step Guidance

1. Review each option and count the number of significant digits in each.

2. Remember that all nonzero digits are significant, zeros between nonzero digits are significant, and trailing zeros in a decimal number are significant.

3. Identify which option has exactly three significant figures.

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Q3. A solution contains 0.825g calcium carbonate. If the calcium carbonate solution contains 125 mg of Ca per 5 mL, how many mL contains 0.825g?

Background

Topic: Unit Conversion and Stoichiometry

This question tests your ability to convert between grams and milligrams, and to use ratios to solve for an unknown volume.

Key Terms and Formulas:

• Unit Conversion:

• Ratio/Proportion: Set up a proportion to solve for the unknown volume.

Step-by-Step Guidance

1. Convert 0.825 g to mg by multiplying by 1000.

2. Set up a proportion using the given concentration (125 mg in 5 mL).

3. Solve for the volume (mL) that contains the calculated mg of Ca.

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Q4. There are 58 counties in California and about 560,000 people in each county. How many million people are in California?

Background

Topic: Multiplication and Scientific Notation

This question tests your ability to multiply large numbers and express the result in millions.

Key Terms:

• Million:

Step-by-Step Guidance

1. Multiply the number of counties by the number of people per county.

2. Divide the result by 1,000,000 to convert to millions.

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Q5. How many inches are in 32.8 cm?

Background

Topic: Unit Conversion

This question tests your ability to convert between centimeters and inches using a conversion factor.

Key Terms and Formula:

• Conversion Factor:

Step-by-Step Guidance

1. Write the given value (32.8 cm).

2. Set up the conversion factor so that cm cancels and inches remain.

3. Multiply and simplify, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q6. How many pounds are in 8.5 kg?

Background

Topic: Unit Conversion

This question tests your ability to convert between kilograms and pounds using a conversion factor.

Key Terms and Formula:

• Conversion Factor:

Step-by-Step Guidance

1. Write the given value (8.5 kg).

2. Set up the conversion factor so that kg cancels and pounds remain.

3. Multiply and simplify, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q7. The density of a certain type of steel is 9.2 g/cm³. What is the mass of 100.0 cm³ chunk of this steel?

Background

Topic: Density Calculations

This question tests your ability to use the density formula to find mass when given volume and density.

Key Terms and Formula:

• Density:

• Rearranged:

Step-by-Step Guidance

1. Write down the given values: density (9.2 g/cm³) and volume (100.0 cm³).

2. Plug these values into the mass formula.

3. Multiply to find the mass, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q8. A solution has a density of 1.22 g/mL. What volume of solution has a mass of 95.7 g?

Background

Topic: Density Calculations

This question tests your ability to use the density formula to find volume when given mass and density.

Key Terms and Formula:

• Density:

• Rearranged:

Step-by-Step Guidance

1. Write down the given values: mass (95.7 g) and density (1.22 g/mL).

2. Plug these values into the volume formula.

3. Divide to find the volume, but do not calculate the final value yet.

Try solving on your own before revealing the answer!

Q9. Which of the following is the SI unit of temperature?

Background

Topic: SI Units

This question tests your knowledge of the International System of Units (SI) for temperature.

Key Terms:

• SI Unit: The standard unit of measurement in the metric system.

Step-by-Step Guidance

1. Recall the SI base unit for temperature.

2. Identify the correct answer from the options provided.

Try solving on your own before revealing the answer!