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Chapter 5: Problem 35

For Exercises \(33-40\), convert the fraction to a decimal and round to the indicated place value. \(\frac{1}{7} ;\) thousandths

Short Answer

Expert verified
0.143

Step by step solution

01

- Divide the Numerator by the Denominator

Divide 1 by 7 using long division or a calculator to find the decimal equivalent. The result of this division is approximately 0.142857.
02

- Identify the Thousandths Place

The thousandths place is the third digit to the right of the decimal point. In the number 0.142857, the digit in the thousandths place is 2.
03

- Round the Decimal

To round to the thousandths place, look at the digit immediately to the right of the thousandths place (which is 8 in this case). Since 8 is greater than or equal to 5, round up the third digit. Therefore, 0.142857 rounded to the nearest thousandths place is 0.143.

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Key Concepts

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

fractions to decimals
One of the fundamental concepts in math is converting fractions to decimals. To convert a fraction like \(\frac{1}{7}\) to a decimal, you perform division: the numerator (top number) divided by the denominator (bottom number). Using long division or a calculator, you find that \(\frac{1}{7}\) equals approximately 0.142857. This number has a repeating pattern because 7 does not divide evenly into 1. Understanding this conversion is crucial for further rounding or using the decimal in calculations. Some tips for converting fractions to decimals include:
  • Use a calculator for complex fractions or long repeats.
  • Identify if the decimal will be terminating (ends) or repeating.
rounding decimals
Rounding decimals helps simplify numbers by keeping them at a specific place value. In the exercise, we rounded the decimal 0.142857 to the thousandths place. Here's how:
Identify the place value you need鈥攊n this case, the thousandths place, which is the third digit to the right of the decimal point.
Look at the digit immediately to the right of the chosen place value (the 'next' digit). In 0.142857, the next digit is 8.
If the next digit is 5 or above, you round up. If it's below 5, you round down. Here, 8 means we round up.
So, 0.142857 rounded to the nearest thousandths place becomes 0.143.
  • Rounding makes numbers easier to work with by reducing the digits while keeping them close to the original value.
  • Always look at the next digit to decide whether to round up or down.
place value
Understanding place value is essential for working with decimals. Each position in a decimal number represents a different place value. Starting from the left of the decimal point, we have:
  • Ones
  • Tenths
  • Hundredths
  • Thousandths
In the number 0.142857, 1 is in the tenths place, 4 is in the hundredths place, and 2 is in the thousandths place. Rounding decisions are based on these place values. It鈥檚 important to:
  • Know the place values to understand the size and precision of numbers.
  • Use place value to properly round and estimate numbers.
Recognizing these values helps in various mathematical operations, including addition, subtraction, and comparing numbers.

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Most popular questions from this chapter

Water flows into a pool at a constant rate. The water level is recorded at several 1-hr intervals. a. From the table, how many inches is the water level rising each hour? b. At this rate, what will the water level be at 1: 00 PM.? c. At this rate, what will the water level be at 3.00 p.M.? $$\begin{array}{c|c} \text { Time } & \text { Water Level } \\ \hline 9: 00 \mathrm{A} . \mathrm{M} & 4.2 \mathrm{in} . \\ \hline 10: 00 \mathrm{A} \ldots & 5.9 \mathrm{in} . \\ \hline 11.00 \mathrm{A} \ldots & 7.6 \mathrm{in} . \\ \hline 12.00 \mathrm{em} . & 9.3 \mathrm{in.} \\ \hline \end{array}$$

What is the least number with three places to the right of the decimal that can be created with the digits 2, 9, and 7? Assume that the digits cannot be repeated.

For Exercises \(43-48\), write the decimal number representing each word name. The number of beehives in the United States is 2.6 million. (Source: U.S. Department of Agriculture)

For Exercises \(83-88\) simplify by $$6.5+\frac{1}{8}\left(\frac{1}{5}\right)^{2}$$

One megawatt (MW) of wind power produces enough electricity to supply approximately 275 homes. For a recent year, the state of Texas produced \(3352 \mathrm{MW}\) of wind power. (Source: American Wind Energy Association) a. About how many homes can be supplied with electricity using wind power produced in Texas? b. The given table outlines new proposed wind power projects in Texas. If these projects are completed, approximately how many additional homes could be supplied with electricity? $$\begin{array}{l|c} \text { Project } & \text { MW } \\ \hline \text { JD Wind IV } & 79.8 \\ \hline \text { Buffalo Gap, Phase II } & 232.5 \\ \hline \text { Lone Star I (3Q) } & 128 \\ \hline \text { Sand Bluff } & 90 \\ \hline \text { Roscoe } & 209 \\ \hline \text { Barton Chapel } & 120 \\ \hline \text { Stanton Wind Energy Center } & 120 \\ \hline \text { Whirlwind Energy Center } & 59.8 \\ \hline \text { Swcetwater V } & 80.5 \\ \hline \text { Champion } & 126.5 \\ \hline \end{array}$$
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