/*! 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 25 What are significant figures? Sh... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

What are significant figures? Show how to indicate the number one thousand to 1 significant figure, 2 significant figures, 3 significant figures, and 4 significant figures. Why is the answer, to the correct number of significant figures, not \(1.0\) for the following calculation? $$ \frac{1.5-1.0}{0.50}= $$

Short Answer

Expert verified
Significant figures are digits in a number that carry meaning and contribute to its measurement precision. To represent one thousand with varying significant figures, we have: \(1\) significant figure: \(1 \times 10^3\); \(2\) significant figures: \(1.0 \times 10^3\); \(3\) significant figures: \(1.00 \times 10^3\); and \(4\) significant figures: \(1.000 \times 10^3\). For the given calculation, \(\frac{1.5-1.0}{0.50}\), after performing the subtraction and division with proper consideration of significant figures, the result is \(1.0\). Contrary to the question, the correct answer is \(1.0\). This might be due to a mistake in the text or an attempt to demonstrate the importance of using significant figures correctly, leading to the right answer, which is \(1.0\).

Step by step solution

01

Understand significant figures

Significant figures are the digits in a measurement or number that carry meaning and contribute to its precision. A number with more significant figures is more precise than a number with fewer significant figures. When performing calculations, it's essential to consider significant figures to avoid losing precision or introducing false precision.
02

Indicate one thousand with varying significant figures

Let's show the number one thousand to 1, 2, 3, and 4 significant figures. \(1\) significant figure: \(1 \times 10^3\) \(2\) significant figures: \(1.0 \times 10^3\) \(3\) significant figures: \(1.00 \times 10^3\) \(4\) significant figures: \(1.000 \times 10^3\)
03

Analyze the given calculation

The given calculation is: \[ \frac{1.5 - 1.0}{0.50} \] First, we'll calculate the numerator and denominator individually, taking care of significant figures.
04

Calculate the numerator

In the numerator, we have: \[ 1.5 - 1.0 \] Both numbers have one decimal place (precision to the tenths), so the answer of the subtraction should also have one decimal place. We get: \[ 1.5 - 1.0 = 0.5 \]
05

Calculate the denominator

The denominator is already given as 0.50, and there is no calculation required.
06

Perform the given calculation

Divide the numerator by the denominator, considering the significant figures: \[ \frac{0.5}{0.50} \] Both the numerator and denominator have one decimal place, so our division result must have at least one decimal place as well. The result of the division is: \[ \frac{0.5}{0.50} = 1.0 \]
07

Understand the "not 1.0" question

The question asks why the answer is not \(1.0\) for the calculation. However, the answer to the given calculation \emph{is} \(1.0\). This might be a mistake in the text of the exercise or an attempt to show that the correct use of significant figures leads to the right answer, which is \(1.0\) indeed.

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 91Ó°ÊÓ!

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

a. How many kilograms are in one teragram? b. How many nanometers are in \(6.50 \times 10^{2}\) terameters? c. How many kilograms are in 25 femtograms? d. How many liters are in \(8.0\) cubic decimeters? e. How many microliters are in one milliliter? f. How many picograms are in one microgram?

Precious metals and gems are measured in troy weights in the English system: \(\begin{aligned} 24 \text { grains } &=1 \text { pennyweight (exact) } \\ 20 \text { pennyweight } &=1 \text { troy ounce (exact) } \\ 12 \text { troy ounces } &=1 \text { troy pound (exact) } \\ 1 \text { grain } &=0.0648 \text { gram } \\ 1 \text { carat } &=0.200 \mathrm{gram} \end{aligned}\) a. The most common English unit of mass is the pound avoirdupois. What is one troy pound in kilograms and in pounds? b. What is the mass of a troy ounce of gold in grams and in carats? c. The density of gold is \(19.3 \mathrm{~g} / \mathrm{cm}^{3} .\) What is the volume of a troy pound of gold?

Which of the following are exact numbers? a. There are \(100 \mathrm{~cm}\) in \(1 \mathrm{~m}\). b. One meter equals \(1.094\) yards. c. We can use the equation \({ }^{\circ} \mathrm{F}=\frac{9 \circ}{2} \mathrm{C}+32\) to convert from Celsius to Fahrenheit temperature. Are the numbers \(\frac{9}{3}\) and 32 exact or inexact? d. \(\pi=3.1415927\).

You have a \(1.0-\mathrm{cm}^{3}\) sample of lead and a \(1.0-\mathrm{cm}^{3}\) sample of glass. You drop each in separate beakers of water. How do the volumes of water displaced by each sample compare? Explain.

In each of the following pairs, which has the greater volume? a. \(1.0 \mathrm{~kg}\) of feathers or \(1.0 \mathrm{~kg}\) of lead b. \(100 \mathrm{~g}\) of gold or \(100 \mathrm{~g}\) of water c. \(1.0 \mathrm{~L}\) of copper or \(1.0 \mathrm{~L}\) of mercury

See all solutions

Recommended explanations on Chemistry Textbooks

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.