Round each number to three significant figures. a. 79,845.82 b. 1.548937×10 7 c. 2.3499999995 d. 0.000045389

Hi everyone for this question we need to round each of the following 22 significant figures. So let's go ahead and get started for part a we have 32,324 the first thing we need to do is convert this to a decimal. So let's do that by putting a decimal here and moving it to the left 1234 units. So when we do that we get 3.2 and we can raise everything else to a power. So this is going to be times 10 to the four For part B We have 2. times 10 to the 5th. So this is already in a decimal which is great. So let's go ahead and take a look at this zero here because it communicates a level of uncertainty. And so we need to look at the next digit which is a five. And when we have a five we can either increase our zero by one or leave it unchanged. So let's go ahead and increase it by one. And when we do that we will get 2.1 which is two significant figures and will raise everything else to a power. So this is going to be times 10 to the fifth for part C it is in decimal but we need to make it to two decimal places. So let's go ahead and move that decimal to the left. And when we do that we move it 12345 units to the left and when we do that we get 4.5 and we can raise everything else to a power. So that's going to be times 10 to the fifth. And for our last one we have a really long decimal. Now we need to move our decimal place to the right so that we can have two significant figures. So we're going to move this 1, 2, 3, 45, 6, 7, 8, 9, 10, 11, 12, 13. So this is going to move 13 places To the right. And so we'll get 9.3 and we'll raise this to a decimal. And because raise this to a power and because we move to the right, this is going to be a negative power. So this is going to be times 10 to the -13. So these are our final answers, rounded to two significant figures. And that is the end of this problem. I hope this was helpful.

Ch.1 - Matter, Measurement & Problem Solving

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Tro 5th Edition

Ch.1 - Matter, Measurement & Problem Solving

Problem 82

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Chapter 1, Problem 82

Round each number to three significant figures. a. 79,845.82 b. 1.548937×10⁷ c. 2.3499999995 d. 0.000045389

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Identify the first three significant figures in each number.

For each number, look at the digit immediately following the third significant figure to determine if rounding is necessary.

If the digit is 5 or greater, round up the third significant figure by one. If it is less than 5, keep the third significant figure as is.

Apply the rounding rule to each number individually.

Rewrite each number with only the first three significant figures, ensuring the correct placement of the decimal point or scientific notation.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in scientific contexts.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified number of significant figures. When rounding, if the digit following the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged. This ensures that the rounded number reflects the appropriate level of precision.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form, using powers of ten. A number is written as a product of a coefficient (between 1 and 10) and a power of ten. This notation is particularly useful for handling very large or very small values, making it easier to perform calculations and maintain significant figures.