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Chapter 1: Problem 57

How many significant digits are there in each measurement below? \(33,002\) miles

Short Answer

Expert verified
The measurement 33,002 miles has 5 significant digits.

Step by step solution

01

Identify Non-Zero Digits

In the number 33,002, identify all the non-zero digits. These are 3, 3, and 2. Non-zero digits are always significant.
02

Analyze Zeroes in the Measurement

The number 33,002 has two zeroes in between the non-zero digits. Zeroes that are between non-zero digits are also considered significant.
03

Count All Significant Digits

Count all the significant digits identified in the previous steps: three non-zero digits and two zeroes between them. This totals to 5 significant digits.

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Key Concepts

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

Non-Zero Digits
Non-zero digits are the backbone of determining significant figures in any number. These are the digits from 1 to 9 and they are always counted as significant. Whether you are working with whole numbers or decimals, these digits never lose their significance. For instance, in the number 33,002, the digits 3, 3, and 2 are non-zero digits and are inherently significant.

Remember this easy rule: whenever you see a non-zero digit, consider it significant without any exceptions. This makes understanding which parts of a numerical measurement matter so much easier.
Significant Figures
Significant figures are the digits in a number that contribute to its accuracy. They are crucial in scientific contexts as they convey the precision of a measured or calculated quantity. Calculating significant figures involves a set of rules including the consideration of non-zero digits, as well as certain zeroes.

In the example of 33,002, all digits contribute to its significant figures. The non-zero digits (3, 3, 2) automatically count, and since the zeroes are between these digits, they also count. Different scenarios can alter how zeroes affect this count, but we'll delve into that more in the upcoming sections.
Mathematical Measurement
Mathematical measurements rely heavily on significant figures to indicate the precision of the measurement. Every digit used conveys essential information about the extent to which the measurement is exact.

For example, distance measurements, like the 33,002 miles, imply a certain degree of accuracy thanks to its significant digits. This helps scientists, engineers, and other professionals convey clear and precise information. It acts as a standardized way to report the reliability and validity of numerical data.
Zeroes in Measurements
Zeroes can either be significant or not depending on their position in a number. They are often the trickiest part of counting significant figures but following a few simple rules can make it easier.

Zeroes between non-zero digits, like the two zeroes in 33,002, are always significant. These zeroes are part of the exact quantity being expressed. On the other hand, trailing zeroes (zeroes at the end of a number with no decimal point) might not be significant, unless specified by a decimal point.

Understanding the role of zeroes helps immensely in determining the precision of measurements and in communicating the accuracy and quality of the data being presented.

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