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Chapter 1: Problem 1

Find the number of significant figures in each number. $$250.03$$

Short Answer

Expert verified
The number 250.03 has five significant figures.

Step by step solution

01

Identifying Non-Zero Digits

Identify all non-zero digits in the number. In 250.03, the non-zero digits are 2, 5, and 3.
02

Identifying Significant Zero Digits

Point out any zero digits that are considered significant. In 250.03, there are zero digits located between the digits 5 and 3, making them significant.
03

Counting Significant Figures

Count all significant digits. Combining significant non-zero digits from Step 1 and significant zero digits from Step 2, there are five significant digits in the number 250.03

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Key Concepts

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

Understanding Non-Zero Digits
Non-zero digits are the heart of any measurement. They are always significant because they represent an actual measurement value. For example, in the number 250.03, the non-zero digits are 2, 5, and 3. Each of these digits contributes to the precision of the number.

When counting non-zero digits in any given number, simply identify all digits from 1 to 9. These are always counted as significant figures. Remember that every non-zero digit counts towards the value's precision and gives us essential information about the size and scale of the measurement.

In short:
  • All digits from 1 to 9 are always significant.
  • Non-zero digits are straightforward to identify in any number since they stand out without confusion.
  • They enhance the accuracy and reliability of numerical data.
The Role of Significant Zeros
Zeros can sometimes be tricky in terms of significance, but understanding their role is crucial. In some contexts, zeros are significant because they describe a precise level of measurement, while other times, they serve as mere placeholders.

When we look at the number 250.03, the zeros are significant because they lie between two non-zero digits (5 and 3). This is a key rule: any zeros between two significant figures are also considered significant. Such zeros help reflect a value's precision and should not be ignored.

Helping clarify the role of zeros:
  • Zeros sandwiched between non-zero digits are significant.
  • Leading zeros, appearing before the first non-zero digit, are not significant.
  • Trailing zeros only count as significant if there's a decimal point present.
Significant zeros are important for giving a precise measure of the exactness of your data.
Counting Significant Figures Effectively
Grasping how to count significant figures is essential for scientific accuracy. It involves summing up both non-zero digits and significant zeros. In the example number 250.03, to count significant figures, we first considered the non-zero digits (2, 5, and 3) and added the zeros between them.

Here鈥檚 a simple breakdown for counting:
  • Identify all non-zero digits and count them as significant.
  • Add any zeros located between these non-zero digits, since they are significant too.
When you tally up the significant figures in 250.03, you find a total of five significant digits.

To perfect counting significant figures, always remember:
  • Start by identifying and counting all non-zero digits.
  • Include all applicable significant zeros.
  • Be mindful of zeros that do not affect the count, such as leading zeros before a decimal point.
This method ensures both precision and reliability in scientific calculations.

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Most popular questions from this chapter

Graph the function by hand. $$f(x)=\left\\{\begin{array}{ll} 1, & x<0 \\ 0, & 0 \leq x<1 \\ -1, & x \geq 1 \end{array}\right.$$

Solve the inequality. Express your answer in interval notation. $$-4(x+2) \geq x+5$$

This set of exercises will draw on the ideas presented in this section and your general math background. Find the intersection of the lines \(x+y=2\) and \(x-y=1\) You will have to first solve for \(y\) in both equations and then use the methods presented in this section. (This is an example of a system of linear equations, a topic that will be explored in greater detail in a later chapter.)

Applications In this set of exercises you will use the concepts of intersection of lines and linear inequalities to study real-world problems. Cost and Revenue In Exercises \(69-72,\) for each set of cost and revenue functions, (a) find the break-even point and (b) calculate the values of \(q\) for cohich retucnue exceeds cost. $$\begin{aligned} &C(q)=3 q+20\\\ &R(q)=6 q \end{aligned}$$

Pricing Tickets Sherman is planning to bring in a jazz group of four musicians for a fund-raising concert at Grand State University. The jazz group charges \(\$ 500\) for an appearance, and dinner will be provided to the musicians at a cost of \(\$ 20\) each. In addition, the musicians will be reimbursed for mileage at a rate of \(\$ 0.30\) permile. The group will be traveling a total of 160 miles. A ticket for the concert will be priced at \(\$ 8 .\) How many people must attend the concert for the university to break even?
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