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Chapter 2: Problem 25

Round off or add zeros to each of the following to three significant figures: a. \(56.855 \mathrm{~m}\) b. \(0.002282 \mathrm{~g}\) c. \(11527 \mathrm{~s}\) d. 8.1 L

Short Answer

Expert verified
a. 56.9 mb. 0.00228 gc. 11500 s or 1.15 x 10^4 sd. 8.10 L

Step by step solution

01

Identify the Number of Significant Figures

Significant figures are the digits that carry meaning contributing to its measurement resolution. The task is to round off or add zeros to make the number three significant figures.
02

Round off 56.855 m

Examine 56.855 m: It has five significant figures. Rounding to three significant figures, 56.855 rounds to 56.9 m. The digit after the third significant figure (8 in this case) is greater than 5, so increase the last retained digit by one.
03

Round off 0.002282 g

Examine 0.002282 g: It has four significant figures. Rounding to three significant figures, 0.002282 rounds to 0.00228 g. The digit after the third significant figure (2 in this case) is less than 5, so there is no change to the last retained figure.
04

Round off 11527 s

Examine 11527 s: It has five significant figures. Rounding to three significant figures, 11527 rounds to 11500 s or in scientific notation, it can be written as 1.15 x 10^4 s. The digit after the third significant figure (2 in this case) is less than 5.
05

Add zeros to 8.1 L

Examine 8.1 L: It has two significant figures. To convert this to three significant figures, add a zero after the last digit, making it 8.10 L.

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Key Concepts

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

Rounding Numbers
Rounding numbers is a crucial skill in math and science. It helps simplify results and make them easier to communicate and work with. When rounding to a specific number of significant figures, you only keep the most important digits. The rule is to look at the digit right after your last significant figure. If it's 5 or above, you round up. If it鈥檚 below 5, you round down. For example, when rounding 56.855 to three significant figures, you keep 56.8 and consider the next digit (5), which tells you to round up to get 56.9. This method allows scientists and students to make their data more manageable and readable.
Measurement Resolution
Measurement resolution refers to the smallest change or increment that a measuring instrument can detect. The more significant figures in a measurement, the higher the resolution. In scientific contexts, higher measurement resolution implies greater precision and accuracy. For instance, measuring a substance as 0.002282 grams to three significant figures gives us 0.00228 grams. Knowing how to determine the right number of significant figures helps in maintaining the integrity of scientific data.
Scientific Notation
Scientific notation is a way to express very large or very small numbers conveniently. It is used to simplify numbers, ensuring they are more manageable and easier to read. This is especially useful in fields like physics and astronomy. For example, the number 11527 seconds rounded to three significant figures can be written as 1.15 x 10^4 seconds. This notation helps in neatly expressing values without using tons of zeros, which can be cumbersome.
Precision
Precision in measurements refers to how close multiple measurements of the same thing are to each other. Precision is connected deeply to significant figures because the number of significant figures in a measurement shows how precise it is. For example, 8.1 liters to three significant figures would be expressed as 8.10 liters. Adding significant figures can often imply a higher level of precision in the measurements. It's important to always report measurements to the correct number of significant figures to accurately represent the precision of the measurement.

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Most popular questions from this chapter

Write the numerical value for each of the following prefixes: a. centi b. tera c. milli d. deci

What is the density \((\mathrm{g} / \mathrm{mL})\) of each of the following samples? a. A lightweight head on a golf club is made of titanium. The volume of a sample of titanium is \(114 \mathrm{~cm}^{3}\) and the mass is \(514.1 \mathrm{~g}\) b. A syrup is added to an empty container with a mass of \(115.25 \mathrm{~g}\). When \(0.100 \mathrm{pt}\) of syrup is added, the total mass of the container and syrup is \(182.48 \mathrm{~g}\). c. A block of aluminum metal has a volume of \(3.15 \mathrm{~L}\) and a mass of \(8.51 \mathrm{~kg}\).

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)

Use metric conversion factors to solve each of the following problems: a. The Daily Value (DV) for phosphorus is \(800 \mathrm{mg}\). How many grams of phosphorus are recommended? b. A glass of orange juice contains \(3.2 \mathrm{dL}\) of juice. How many milliliters of orange juice are in the glass? c. A package of chocolate instant pudding contains \(2840 \mathrm{mg}\) of sodium. How many grams of sodium are in the pudding? d. A jar contains \(0.29 \mathrm{~kg}\) of olives. How many grams of olives are in the jar?

Solve each of the following problems using one or more conversion factors: a. Wine is \(12 \%\) alcohol by volume. How many milliliters of alcohol are in a 0.750-L bottle of wine? b. Blueberry high-fiber muffins contain \(51 \%\) dietary fiber by mass. If a package with a net weight of 12 oz contains six muffins, how many grams of fiber are in each muffin? c. A jar of crunchy peanut butter contains \(1.43 \mathrm{~kg}\) of peanut butter. If you use \(8.0 \%\) of the peanut butter for a sandwich, how many ounces of peanut butter did you take out of the container? d. In a candy factory, the nutty chocolate bars contain \(22.0 \%\) pecans by mass. If \(5.0 \mathrm{~kg}\) of pecans were used for candy last Tuesday, how many pounds of nutty chocolate bars were made?
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