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 approximately 0.2432, 0.4286, 0.6429, -20.6, and -0.8462. Each fraction was converted by dividing the numerator by the denominator. Some decimals are repeating while others are terminating.
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Divide the numerator by the denominator for each rational number.
37 9 ≈ 0.243
42 18 = 7 3 ≈ 0.429
14 9 ≈ 0.643
5 − 103 = − 20.6
− 13 11 ≈ − 0.846
The decimal forms are: 0.243 , 0.429 , 0.643 , − 20.6 , − 0.846 .
Explanation
Understanding the Problem We need to convert the given rational numbers into decimal form. This involves dividing the numerator by the denominator for each fraction.
Converting 9/37 to Decimal For the first fraction, 37 9 , we divide 9 by 37. The result is approximately 0.243243243...
Converting 18/42 to Decimal For the second fraction, 42 18 , we divide 18 by 42. This fraction can be simplified to 7 3 . Dividing 3 by 7 gives approximately 0.428571428...
Converting 9/14 to Decimal For the third fraction, 14 9 , we divide 9 by 14. The result is approximately 0.642857142...
Converting -103/5 to Decimal For the fourth fraction, 5 − 103 , we divide -103 by 5. The result is -20.6.
Converting -11/13 to Decimal For the fifth fraction, − 13 11 , we divide -11 by 13. The result is approximately -0.846153846...
Final Decimal Forms Therefore, the decimal forms of the given rational numbers are: (1) 37 9 ≈ 0.243243243 (2) 42 18 ≈ 0.428571428 (3) 14 9 ≈ 0.642857142 (4) 5 − 103 = − 20.6 (5) − 13 11 ≈ − 0.846153846
Examples
Converting fractions to decimals is a fundamental skill with many practical applications. For instance, when you're cooking and need to adjust ingredient quantities, you might need to convert a fractional measurement (like 3 2 cup) to a decimal to use a digital scale. Similarly, in finance, understanding decimal equivalents of fractions is crucial for calculating interest rates or discounts. For example, a discount of 4 1 off an item is the same as a 25% discount, or 0.25 in decimal form. These conversions make calculations easier and more precise in everyday situations.
