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Chapter 1: Q3. (page 17)

Why is it incorrect to think that the more digits you include in your answer, the more accurate it is?

Short Answer

Expert verified

Adding more digits to an answer does not increase its accuracy.

Step by step solution

01

Step 1. Disadvantage of adding more digits in the answer

Including too many digits in the answer does not increase its accuracy. The accuracy of the answer only depends on the physical measurement on which it is based.

Adding many digits requires greater accuracy, which may not be possible with the given measurements.

02

Step 2. Examples of problems with more digits in the answer

Consider a rectangle of length 1.25 cm and breadth 1.1 cm. The area of this rectangle is 1.375 cm2.

The scale on which the area is measured is accurate only up to 0.1 cm2. Therefore, in this case, the answer will be 1.4 cm2, and adding more digits will not make it more accurate.

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Most popular questions from this chapter

Write out the following numbers in full with the correct number of zeros: (a)8.69×104, (b)9.1×103, (c)8.8×10-1, (d)4.76×102, and (e)3.62×10-5.

Recent findings in astrophysics suggest that the observable universe can be modeled as a sphere of radiusR=13.7×109lightyears=13.0×1025mwith an average total mass density of about1×10-26kg/m3. Only about 4% of total mass is due to “ordinary” matter (such as protons, neutrons, and electrons). Estimate how much ordinary matter (in kg) there is in the observable universe. (For the light- year, see the Problem19.)

A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CD’s information at a constant rate of 1.4 megabits per second. How many minutes does the player take to read the entire CD?

Estimate how many hours it would take to run (at 10 km/h) across the U.S from New York to California.

(Note: Remember that for rough estimates, only round numbers are needed both as input to calculations and as final results.)

Estimate the number of dentists (a) in San Francisco and (b) in your town or city.
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