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Chapter 2: Problem 9

Round each of the following numbers to three significant figures: (a) \(93.246\) (b) \(0.02857\) (c) \(4.644\) (d) \(34.250\)

Short Answer

Expert verified
(a) 93.2, (b) 0.0286, (c) 4.64, (d) 34.3

Step by step solution

01

- Rounding 93.246

Identify the first three significant figures in the number 93.246. They are 9, 3, and 2. The fourth significant figure is 4, which is less than 5, so we do not round up. Thus, 93.246 rounded to three significant figures is 93.2.
02

- Rounding 0.02857

Identify the first three significant figures in the number 0.02857. They are 2, 8, and 5. The fourth significant figure is 7, which is more than 5, so we round up. Thus, 0.02857 rounded to three significant figures is 0.0286.
03

- Rounding 4.644

Identify the first three significant figures in the number 4.644. They are 4, 6, and 4. The fourth significant figure is 4, which is less than 5, so we do not round up. Thus, 4.644 rounded to three significant figures is 4.64.
04

- Rounding 34.250

Identify the first three significant figures in the number 34.250. They are 3, 4, and 2. The fourth significant figure is 5, which is exactly 5, so we round up. Thus, 34.250 rounded to three significant figures is 34.3.

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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 very useful skill for simplifying numbers, especially when you don't need extreme precision. It helps in easier calculations and understanding. Here are some basic rules for rounding numbers:
  • If the digit to the right of your target place is less than 5, leave the target digit as it is.

  • If the digit to the right of your target place is 5 or greater, increase the target digit by one.

Let's see an example from our problem:
(a) For 93.246, we are asked to round to three significant figures. The first three digits are 9, 3, and 2. The next digit is 4, which is less than 5. Thus, 93.246 rounded to three significant figures is 93.2.
Significant Digits
Significant digits (or figures) are the important digits in a number that contribute to its precision. They start from the first non-zero digit on the left and continue to the right.
  • For example, in 0.02857, the first non-zero digit is 2. So, the significant digits are 2, 8, and 5.

  • Zeros in between non-zero digits are also significant, such as in 405, which has three significant digits.

Let’s apply it to our exercise:
(b) For 0.02857, the significant digits are 2, 8, and 5. The next digit is 7, which means we round up. Therefore, it rounds to 0.0286.
Precision in Measurements
Precision in measurements refers to how detailed and exact a measurement is. It’s important when you need to be very specific about a quantity.
  • The more significant digits you include, the higher the precision.

  • For example, using five significant digits instead of three gives a more accurate measurement.

Consider step 3 from our exercise:
(c) For 4.644, the significant numbers are 4, 6, and 4. Since the next digit is 4, we do not round up. Therefore, 4.644 rounded to three significant figures is 4.64.

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Most popular questions from this chapter

An extra-strength aspirin tablet contains \(0.500 \mathrm{~g}\) of the active ingredient, acetylsalicylic acid. Aspirin strength used to be measured in grains. If 1 grain \(=60 \mathrm{mg}\), how many grains of the active ingredient are in 1 tablet? (Report your answer to three significant figures.)

A \(25.2-\mathrm{mL}\) sample of kerosene was determined to have a mass of \(20.41 \mathrm{~g}\). What is the density of kerosene?

Will a hollow cube with sides of length \(0.50 \mathrm{~m}\) hold \(8.5 \mathrm{~L}\) of solution? Depending on your answer, how much additional solution would be required to fill the container or how many times would the container need to be filled to measure the \(8.5 \mathrm{~L}\) ?

How many days would it take for a crepe myrtle tree to grow 1 \(\mathrm{cm}\) in height if it grows \(3.38\) feet per year? (Report your answer to three significant figures)

In 2005 , Jarno Trulli was the pole winner of the U.S. Grand Prix Race with a speed of \(133 \mathrm{mi}\) per hr. What was his speed in \(\mathrm{cm} / \mathrm{s}\) ?
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