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Chapter 2: Problem 11

Write the number 87,449 in scientific notation with four significant figures.

Short Answer

Expert verified
87,449 in scientific notation is 8.745 x 10^4.

Step by step solution

01

Identify the Significant Figures

First, identify the four significant figures in the number 87,449. They are 8, 7, 4, and 4.
02

Convert to a Decimal

Place a decimal after the first significant figure. This converts the number into 8.7449.
03

Round to Desired Significant Figures

Since we need four significant figures, round 8.7449 to 8.745.
04

Count the Exponent for Scientific Notation

Count how many places the decimal moved. Starting from 87,449 and moving the decimal 4 places to the left gives us 8.745 x 10^4.

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Key Concepts

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

Significant Figures
Understanding significant figures is key in scientific notation. They help indicate the precision of a number. In the example of 87,449, the significant figures are comprised of the digits that are meaningful in terms of accuracy. Here, the significant figures are 8, 7, 4, and another 4. A few tips to remember:
  • Leading zeros are never significant.
  • All non-zero digits are always significant.
  • Any zeros between significant figures are also significant.
Recognizing these figures isn't just about picking digits, but understanding which numbers affect measurement precision.
Decimal Conversion
Converting a number into decimal form is a crucial step in scientific notation. Here, you take the number 87,449 and place a decimal point after the first significant digit: 8.7449. Steps to keep in mind:
  • Identify the first significant figure.
  • Place the decimal point immediately after this digit.
  • Ensure all necessary figures are included in the new decimal form.
This decimal conversion helps in fitting the number into the standardized scientific notation format.
Rounding Numbers
Rounding is essential in scientific notation to meet the specified significant figures. In our example, you have 8.7449 from the decimal conversion step. Important rounding tips:
  • Look at the digit following your final significant figure (here, after the fourth digit).
  • If this digit is 5 or more, round up the last significant figure.
  • If it's less than 5, leave the final figure as is.
For 8.7449, since the digit after four figures is 9, you round up to 8.745. This ensures accuracy while maintaining precision.
Exponents
Exponents come into play when transforming a decimal into scientific notation. They indicate how many places the decimal has moved. In practice:
  • Count the number of places the decimal moves to get from the original number to its new position.
  • Each move to the left increases the exponent by one.
  • The value is then expressed as a power of ten.
For the number 87,449, moving the decimal four places left to 8.745 results in an exponent of 4, so the scientific notation is written as 8.745 x 10^4. This method streamlines how large numbers are presented and interpreted.

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Most popular questions from this chapter

Perform the following conversions. a) \(833 \mathrm{~ns}\) to seconds b) \(5.809 \mathrm{~s}\) to milliseconds c) \(2.77 \times 10^{6} \mathrm{~s}\) to megaseconds

What is the area in square millimeters of a rectangle whose sides are \(2.44 \mathrm{~cm} \times 6.077 \mathrm{~cm}\) ? Express the answer to the proper number of significant figures.

Perform the following conversions. a) \(255^{\circ} \mathrm{F}\) to degrees Celsius b) \(-255^{\circ} \mathrm{F}\) to degrees Celsius c) \(50.0^{\circ} \mathrm{C}\) to degrees Fahrenheit d) \(-50.0^{\circ} \mathrm{C}\) to degrees Fahrenheit 2\. Perform the following conversions. a) \(1,065^{\circ} \mathrm{C}\) to degrees Fahrenheit b) \(-222^{\circ} \mathrm{C}\) to degrees Fahrenheit c) \(400.0^{\circ} \mathrm{F}\) to degrees Celsius d) \(200.0^{\circ} \mathrm{F}\) to degrees Celsius

Fill in the blank: \(1 \mathrm{Ms}=\) ______ ns.

What is the volume in cubic centimeters of a cube with sides of \(0.774 \mathrm{~m}\) ? Express the answer to the proper number of significant figures.
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