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A machinist has a sophisticated micrometer that can measure the diameter of a drill bit to \(1 / 10,000\) of an inch. What is the maximum number of significant figures that should be reported if the approximate diameter of the drill bit is (a) \(0.0001\) inches, (b) \(0.1\) inches, (c) 1 inch.

Short Answer

Expert verified
The maximum number of significant figures for the drill bit diameters are: (a) 1, (b) 1, (c) 1.

Step by step solution

01

Understanding significant figures

Significant figures are the digits in a number that carry meaningful information about its precision. For zero measurements, significant figures start after the first non-zero digit. For non-zero measurements, all digits are significant.
02

Drill bit diameter - 0.0001 inches

For a drill bit diameter of 0.0001 inches, we notice that there is one non-zero digit, hence there is only 1 significant figure.
03

Drill bit diameter - 0.1 inches

For a drill bit diameter of 0.1 inches, we can see there is one non-zero digit. Accordingly, there is just 1 significant figure in this measurement.
04

Drill bit diameter - 1 inch

For a drill bit diameter of 1 inch, there is one non-zero digit. Therefore, this measurement has 1 significant figure.

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Key Concepts

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

Measurement Precision
Measurement precision refers to how close a set of measurements are to each other and to the actual or true value. When dealing with precise measurements, even the tiniest difference matters. Precision is crucial in engineering and scientific experiments. It dictates the reliability and repeatability of a measurement.

The precision of a measuring device depends on its smallest unit of measurement. For example:
  • A ruler with millimeter markings has a precision of 1 mm.
  • A digital scale that measures to the nearest gram has a precision of 1 g.
  • A micrometer that measures to 0.0001 inches reflects very high precision.
Precision is essential for quality control, as imprecise measurements can lead to significant errors. When a precision requirement is specified, it ensures consistency across measurements. This can be vital in fields where exactness is key, such as in manufacturing parts to fit together perfectly.
Micrometer Usage
Micrometers are precision measuring tools used for accurately gauging small distances or thicknesses. They often measure to one thousandth of a millimeter or 0.0001 inches, providing high precision in engineering and mechanical tasks.

To use a micrometer:
  • Ensure it is clean and calibrated.
  • Place the object between the spindle and anvil.
  • Rotate the ratchet until the object is gently held.
  • Read the scale on the barrel for accurate measurement.
It's important to use a micrometer correctly to ensure the accuracy of the measurement. Misuse or failure to calibrate can lead to inaccurate readings.

Micrometers come in various types:
  • Outside micrometers for measuring external dimensions.
  • Inside micrometers for measuring internal dimensions.
  • Depth micrometers for measuring depths.
Being skilled in using a micrometer can prevent costly errors in fields like manufacturing and engineering, where precision is paramount.
Significant Figures in Engineering
Significant figures are the digits in a number that convey meaningful information about its precision. In engineering, reporting measurements with correct significant figures is crucial for accuracy and clarity.

When determining significant figures:
  • Non-zero digits are always significant.
  • Any zeros between significant digits are significant.
  • Leading zeros are not significant as they are merely placeholders.
  • Trailing zeros in a decimal number are significant.
In calculations, the result should not contain more significant figures than the measurement with the least number of significant figures. This prevents implied false precision.

For instance, when measuring a drill bit diameter:
  • A measurement of 0.0001 inches with just one non-zero digit has 1 significant figure.
  • A measurement of 0.1 inches similarly has 1 significant figure as the zero is merely a placeholder.
  • A whole number like 1 inch, without further decimals, also counts as near zero significant digits after rounding to 1 significant figure.
Understanding and applying the rules of significant figures accurately ensures consistency and precision in engineering calculations.

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Most popular questions from this chapter

Stephanie knew Adam, the environmental manager, would not be pleased with her report on the chemical spill. The data clearly indicated that the spill was large enough that regulations required it to be reported to the state. When Stephanie presented her report to Adam, he lost his temper. "A few gallons over the limit isn't worth the time it's going to take to fill out those damned forms. Go back to your desk and rework those numbers until it comes out right." What should Stephanie do? \({ }^{14}\) a. Tell Adam that she will not knowingly violate state law and threaten to quit. b. Comply with Adam's request since he is in charge and will suffer any consequences. c. Send an anonymous report to the state documenting the violation. d. Go over Adam's head and speak to his supervisor about the problem.

Calculate with the correct significant figures: (a) 10/6, (b) \(10.0 / 6\), (c) \(10 / 6.0\), (d) 10./6.0, and (e) 10.0/6.00.

You are browsing the Internet and find some units conversion software that may be useful in this course. You would like to download the software on your PC at school and use it in this course. What do you do? a. Check with the Internet site to make sure this software is freeware for your use in this course. b. Just download the software and use it because no one will know. c. Download the software at home and bring it to school. d. Never use software found on the Internet.

Calculate with the correct significant figures: (a) \(100 /\left(2.0 \times 10^{2}\right)\), (b) \(1.0 \times 10^{2} /\) \(\left(2.0 \times 10^{2}\right)\). (A: 0.5, 0.50.)

Suppose the formula for weight of the gas was \(G=W^{b}\), where \(b\) is can be varied in the range \(0.50-0.75\). Graph the range of a \(3.69 \times 10^{3} \mathrm{lbm}\) car as a function of \(b\). Exercises 20-23: These exercises are concerned with bungee jumping as displayed in the figure. At full stretch, the elastic rope of original length \(L\) stretches to \(L+X\). For a person whose weight is \(W\) lbf and a cord with a stiffness \(K \mathrm{lbf} / \mathrm{ft}\), the extension \(X\) is given by the following formula: $$ \mathrm{X}=\frac{\mathrm{W}}{\mathrm{K}}+\sqrt{\frac{\mathrm{W}^{2}}{\mathrm{~K}^{2}}+\frac{2 \mathrm{~W} \times \mathrm{L}}{\mathrm{K}}} $$ which can be written as a spreadsheet equation as: \(X=W / K+\operatorname{sqrt}\left(W^{\wedge} 2 / K^{\wedge} 2+2\right.\) * \(\left.W{ }^{*} L / K\right)\).

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