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Chapter 5: Problem 145

Explain how to write a rational number as a decimal.

Short Answer

Expert verified
A rational number can be converted into a decimal by performing the operation of division. For example, the rational number 3/4 is equal to the decimal 0.75. Some rational numbers, when converted to decimals, result in a repeating pattern, such as 1/3 = 0.333333...

Step by step solution

01

- Understand the problem

You need to comprehend that all rational numbers can be written as a fraction, which in turn can be a division problem.
02

- Convert Fraction into Division

For instance, if you have the rational number \(\frac{3}{4}\), you can rewrite this as the division problem 3 divided by 4, or 3/4.
03

- Execute the Division

Perform the division. Divide the numerator (3) by the denominator (4). In the case of the fraction \(\frac{3}{4}\), this results in the decimal 0.75.
04

- Express as Decimal

Once you have carried out the division, you can express the result as a decimal. So, the rational number \(\frac{3}{4}\) is equivalent to the decimal 0.75.
05

- Interpret repeating decimals

For some rational numbers, the decimal may go on forever. Recognize these as repeating decimals. For instance, \(\frac{1}{3}\) is equal to 0.333333...

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Most popular questions from this chapter

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(0.0007,-0.007,0.07,-0.7, \ldots\)

If you are given a sequence that is arithmetic or geometric, how can you determine which type of sequence it is?

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3, r=-2\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{6}\), when \(a_{1}=-2, r=-3\).

What is the common difference in an arithmetic sequence?
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