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Chapter 2: Problem 115

A balance measures mass to \(0.001 \mathrm{~g}\). If you determine the mass of an object that weighs about \(31 \mathrm{~g}\), would you record the mass as \(31 \mathrm{~g}, 31.1 \mathrm{~g}, 31.08 \mathrm{~g}, 31.075 \mathrm{~g},\) or \(31.0750 ?\) Explain your choice by writing two to three complete sentences that describe your thinking. (2.3)

Short Answer

Expert verified
The correct mass to record is 31.075 g as it matches the balance's precision of measuring up to 0.001 grams.

Step by step solution

01

Understand the Precision of the Balance

The balance measures mass to the nearest 0.001 grams. This means the balance reads measurements to three decimal places.
02

Determine the Appropriate Level of Detail

When recording the mass, we can only be as precise as the balance allows. Given that the balance can measure up to three decimal places, the recorded mass must also reflect this precision.
03

Evaluate the Options

Among the options provided (31 g, 31.1 g, 31.08 g, 31.075 g, 31.0750 g), only the measurement with three decimal places aligns with the balance's precision.
04

Select the Correct Measurement

Therefore, the appropriate measurement to record is 31.075 g, since it correctly reflects the precision of the balance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

significant figures
Understanding significant figures is crucial in scientific measurements. Significant figures include all the digits that are known precisely, plus one last digit that is estimated. For instance, in the number 31.075, all five figures are significant. Knowing how many significant figures to use helps in ensuring precision and accuracy in measurements.
  • When you make a measurement, the digits you record belong to the significant figures.
  • In the context of mass measurement, the balance precision dictates the number of significant figures you can correctly record.
  • For the given balance, which measures up to 0.001 grams, 31.075 grams would have five significant figures.
Hence, the appropriate way to report the mass of the object in the given exercise, based on balance precision, would be 31.075 grams.
decimal places
Decimal places refer to the number of digits to the right of the decimal point in a number. They are significant in scientific measurements because they help in defining the precision of the recorded value.
  • The number of decimal places you use should match the precision of the measuring instrument.
  • In our example, the balance reads measurements up to three decimal places (0.001 grams).
  • Recording more decimal places than the instrument's precision gives false precision, while fewer decimal places undervalue the precision of the instrument.
Thus, the correct record for the mass should align with the available three decimal places of the balance 鈥� hence, 31.075 grams.
mass measurement
Mass measurement is a fundamental aspect of many scientific experiments and procedures. It involves determining the amount of matter in an object, typically using a balance.
  • Precise measurement tools, such as the balance mentioned, help ensure that the mass is recorded accurately.
  • The precision of the balance dictates how detailed the recorded measurement should be.
  • In this exercise, because the balance measures to the nearest 0.001 grams, it is crucial to record the mass with the same level of precision.
So, for an object that weighs about 31 grams, the mass must be recorded as 31.075 grams to reflect the precision of the balance accurately.
balance precision
Balance precision is the smallest increment that a balance can measure. It determines the level of detail and exactness in the measurement readings.
  • For this balance, the smallest unit it measures is 0.001 grams, meaning it can measure and display values to three decimal places.
  • Precision is essential to avoid ambiguities in scientific recordings and ensures consistency across multiple measurements.
  • Using the correct precision shows that you understand the capabilities of your measuring instrument and can properly interpret the results it gives.
Therefore, in recording the mass of an object using a balance with 0.001 grams precision, it should reflect exactly 31.075 grams, maintaining the instrument鈥檚 precision.

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Most popular questions from this chapter

Using conversion factors, solve each of the following clinical problems: a. The physician has ordered \(1.0 \mathrm{~g}\) of tetracycline to be given every six hours to a patient. If your stock on hand is 500 -mg tablets, how many will you need for one day's treatment? b. An intramuscular medication is given at \(5.00 \mathrm{mg} / \mathrm{kg}\) of body weight. What is the dose for a 180 -lb patient? c. A physician has ordered \(0.50 \mathrm{mg}\) of atropine, intramuscularly. If atropine were available as \(0.10 \mathrm{mg} / \mathrm{mL}\) of solution, how many milliliters would you need to give? d. During surgery, a patient receives \(5.0 \mathrm{pt}\) of plasma. How many milliliters of plasma were given?

Calculate the volume of the samples in a. and \(\mathrm{b},\) and the mass of those in c. and d.: a. What is the volume of \(1.22 \mathrm{~g}\) of a solid with a density of \(0.92 \mathrm{~g} / \mathrm{mL} ?\) b. What is the volume of \(0.20 \mathrm{~kg}\) of a solid with a density of \(3.0 \mathrm{~g} / \mathrm{mL} ?\) c. What is the mass, in kilograms, of \(30 \mathrm{~mL}\) of a liquid with a density of \(4.3 \mathrm{~g} / \mathrm{mL} ?\) d. What is the mass, in grams, of \(0.03 \mathrm{~L}\) of a liquid with a density of \(0.83 \mathrm{~g} / \mathrm{mL} ?\)

Write the equality and two conversion factors for each of the following pairs of units: a. centimeters and meters b. nanograms and grams c. liters and kiloliters d. seconds and milliseconds

Perform each of the following conversions using metric conversion factors: a. \(44.2 \mathrm{~mL}\) to liters b. \(8.65 \mathrm{~m}\) to nanometers c. \(5.2 \times 10^{8} \mathrm{~g}\) to megagrams d. 0.72 ks to milliseconds

Write the equality and two conversion factors, and identify the numbers as exact or give the number of significant figures for each of the following: a. A bee flies at an average speed of \(3.5 \mathrm{~m}\) per second. b. The Daily Value (DV) for potassium is \(3.5 \mathrm{~g}\). c. An automobile traveled \(26.0 \mathrm{~km}\) on \(1 \mathrm{~L}\) of gasoline. d. Silicon makes up \(28.2 \%\) by mass of Earth's crust.
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