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Chapter 1: Problem 46

The number of significant figures in \(0.007 \mathrm{~m}^{2}\) is (a) 1 (b) 2 (c) 3 (d) 4

Short Answer

Expert verified
The number of significant figures in \(0.007 \mathrm{~m}^{2}\) is 1. So, the correct answer is option (a).

Step by step solution

01

Analyze the number

In the given number \(0.007 \mathrm{~m}^{2}\), there are a number of leading zeroes before we find a non-zero digit. Remember that leading zeroes do not count as significant figures.
02

Identify Non-Zero Numbers

The non-zero number in the given number is 7 which is considered as a significant figure.
03

Count the Significant Figures

Count the significant figures observed from step 2 - only non-zero numbers and the zeroes between non-zero numbers or after the decimal point if it is not a leading zero. Here we have only one non-zero digit, which means there is only one significant figure.

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Key Concepts

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

Leading Zeros
In the realm of significant figures, understanding the role of leading zeros is crucial. Leading zeros are simply the zeros that come before the first non-zero digit in a decimal number. They act as placeholders and do not have any significance in terms of value. For instance, in the number \(0.007\), the zeros before the seven are leading zeros. These zeros are important for positioning the decimal point but are not counted as significant figures. This rule helps standardize calculations and ensures consistency when measuring and rounding numbers. Remember, leading zeros are only relevant for maintaining the correct decimal placement and not for determining the number of significant figures.
Non-Zero Digits
Non-zero digits are the numbers from 1 to 9, and they are always counted when determining significant figures. No matter their position in a number, each non-zero digit is considered significant. For example, in the number \(0.007\), the digit 7 is the only non-zero digit and is automatically counted as a significant figure. This principle simplifies the process of identifying significant figures: if you spot a non-zero digit, it counts. In scientific measurements, these digits are crucial for accuracy, as they convey the true value of what is being measured without any ambiguity. Identifying non-zero digits ensures that we correctly interpret and express numerical data.
Sig Fig Rules for Decimals
When dealing with decimals, there are specific rules for counting significant figures that ensure numeric precision. Here鈥檚 a quick guide:
  • All non-zero digits are counted as significant figures. So, every digit from 1-9 matters.
  • Leading zeros are not counted as significant figures. They are just placeholders and can be ignored in the count.
  • Trailing zeros (those at the end of a number) can be significant if they are to the right of a decimal point. For example, in \(0.0070\), the trailing zero is significant.
  • Zeros between non-zero digits are always significant. E.g., in \(2.03\), the zero is included in the significant figures count.
      • Being mindful of these rules helps in determining the accuracy of measurements expressed as decimals. This is especially important in fields requiring precision, like science and engineering.

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Most popular questions from this chapter

Conversion of \(1 \mathrm{MW}\) power on a new system having basic units of mass, length and time as \(10 \mathrm{~kg}\), \(1 \mathrm{dm}\) and 1 minute respectively is (a) \(2.16 \times 10^{12}\) unit (b) \(1.26 \times 10^{12}\) unit (c) \(2.16 \times 10^{10}\) unit (d) \(2 \times 10^{14}\) unit

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