Practice Set 1.3
1. Write the following rational numbers in decimal form.
(1) [tex]$\frac{9}{37}$[/tex]
(2) [tex]$\frac{18}{42}$[/tex]
(3) [tex]$\frac{9}{14}$[/tex]
(4) [tex]$\frac{-103}{5}$[/tex]
(5) [tex]$-\frac{11}{13}$[/tex]
Answer (2)
The decimal forms of the given rational numbers are: 37 9 ≈ 0.243243... , 42 18 = 0.428571... , 14 9 ≈ 0.642857... , 5 − 103 = − 20.6 , and − 13 11 ≈ − 0.846153... .
;
Convert each rational number to its decimal form by dividing the numerator by the denominator.
37 9 = 0.243243...
42 18 = 7 3 = 0.428571...
14 9 = 0.642857...
5 − 103 = − 20.6
− 13 11 = − 0.846153... 37 9 = 0.243243... , 42 18 = 0.428571... , 14 9 = 0.642857... , 5 − 103 = − 20.6 , − 13 11 = − 0.846153...
Explanation
Understanding the Problem We need to convert the given rational numbers into their decimal representations. This involves dividing the numerator by the denominator for each fraction.
Converting 9/37 to Decimal For the first fraction, 37 9 , we perform the division 9 ÷ 37 . The result is approximately 0.243243243... , which is a repeating decimal.
Converting 18/42 to Decimal Next, we convert 42 18 to a decimal. First, we simplify the fraction to 7 3 . Then, we divide 3 ÷ 7 , which gives us approximately 0.42857142857... , a repeating decimal.
Converting 9/14 to Decimal For 14 9 , we perform the division 9 ÷ 14 . This results in approximately 0.64285714285... , another repeating decimal.
Converting -103/5 to Decimal Now, we convert 5 − 103 to a decimal. Dividing − 103 by 5 gives us − 20.6 .
Converting -11/13 to Decimal Finally, we convert − 13 11 to a decimal. Dividing − 11 by 13 gives us approximately − 0.84615384615... , a repeating decimal.
Final Answer Therefore, the decimal forms of the given rational numbers are: 37 9 = 0.243243243... 42 18 = 0.42857142857... 14 9 = 0.64285714285... 5 − 103 = − 20.6 − 13 11 = − 0.84615384615...
Examples
Converting fractions to decimals is a fundamental skill with many practical applications. For example, when you're cooking and need to adjust ingredient quantities, you might need to convert a fraction of a cup to a decimal to use a measuring spoon. Similarly, in finance, understanding decimal equivalents of fractions helps in calculating interest rates or discounts. Imagine you want to calculate a 1/3 discount on an item priced at $60. Converting 1/3 to approximately 0.333, you can easily find the discount amount by multiplying $60 by 0.333, which equals $20. Thus, the discounted price is $40.
