/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Determine the precision of each ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 6

Determine the precision of each measurement. \(6.010 \mathrm{~cm}\)

Short Answer

Expert verified
The precision of \(6.010 \mathrm{~cm}\) is four significant figures.

Step by step solution

01

Understand the Concept

Precision in the context of measurement refers to the detail with which the measurement is reported. It is often indicated by the number of significant figures in the measurement.
02

Analyze the Given Measurement

Examine the given measurement: \(6.010 \mathrm{~cm}\). It is important to identify how many significant figures are present in this measurement.
03

Count the Significant Figures

The number \(6.010\) contains four digits. According to the rules of significant figures, all the non-zero digits (6, 1) and any zeros between them or at the end in a decimal context are significant. Hence, all four digits in \(6.010\) are significant, making it a four-significant-figure measurement.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Significant Figures
Significant figures are digits in a number that contribute to its precision. Understanding which digits are significant is crucial when reporting measurements.
This includes:
  • All non-zero digits (e.g., 1, 6 in 6.010 cm).
  • Any zeros between significant digits (e.g., the zero between 1 and 6 in 6.010 cm).
  • Zeros at the end of a number in a decimal form, which indicate precision, like the zero in 6.010 cm.
Thus, each digit in a number that aids in accurately presenting the measurement is vital, adding to the measurement's precision. For example, in the measurement 6.010 cm, the precision is reflected through its four significant figures.
Measurement Reliability
Measurement reliability refers to the consistency and dependability of measurement results. When you take a measurement, having more significant figures generally suggests better precision and reliability.
This ensures that the measurement is consistent across different instances.
  • Measurements with more significant figures indicate less error and greater confidence in the data.
  • High reliability reduces deviations between repeated measurements of the same quantity.
  • Reliable measurements provide a foundation for making accurate calculations and conclusions.
When you encounter a measurement like 6.010 cm with four significant figures, you're looking at a reliable and precise entry that minimizes potential error.
Decimal Representation
Decimal representation is a method used to express numbers and refinements in fractional data. This system relies heavily on significant figures to showcase precision effectively.
Sometimes decimal places are used to express the precision of a measurement.
  • Decimals allow for smoother and more accurate expressions of numbers.
  • They highlight the significance of figures based on their position, such as zeros placed after a decimal point.
  • For instance, in 6.010 cm, each figure represents a crucial aspect of the measurement's accuracy, especially the digit zero at the end, which shows that the measurement is precisely 6.010 and not 6.01.
Decimals are not just placeholders; they're essential in indicating how exact a measurement like 6.010 cm really is, and thus aid in interpreting and utilizing the data correctly.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Use the rules for division of measurements to divide. $$ \frac{8800 \mathrm{mi}}{8.5 \mathrm{~h}} $$

Determine the precision of each measurement. \(0.007 \mathrm{~m}\)

Use the rules for division of measurements to divide. $$ \frac{4960 \mathrm{ft}}{2.95 \mathrm{~s}} $$

Use the rules for multiplication and division of measurements to find the value of each of the following. $$ \frac{48.9 \mathrm{~kg}}{(1.5 \mathrm{~m})(3.25 \mathrm{~m})} $$

Use the rules for addition of measurements to add each set of measurements. $$ 36.8 \mathrm{~m} ; 147.5 \mathrm{~cm} ; 1.967 \mathrm{~m} ; 125.0 \mathrm{~m} ; 98.3 \mathrm{~cm} $$
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Fundamentals of Physics

Read Explanation

Radiation

Read Explanation

Work Energy and Power

Read Explanation

Modern Physics

Read Explanation

Electromagnetism

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.