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Chapter 5: Problem 29

In the following exercises, convert each decimal to a fraction or mixed number. $$15.7$$

Short Answer

Expert verified
15 \(\frac{7}{10}\)

Step by step solution

01

- Identify the Decimal

Recognize that the number to be converted is 15.7.
02

- Write as a Fraction

Write 15.7 as a mixed number. This is a combination of a whole number and a fraction. So, 15.7 can be written as 15 + 0.7.
03

- Convert Decimal to Fraction

Convert 0.7 into a fraction by observing that 0.7 equals \(\frac{7}{10}\).
04

- Combine the Whole Number and Fraction

Combine the whole number and the fraction to form the mixed number. Therefore, 15.7 converts to 15 \(\frac{7}{10}\).

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Key Concepts

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

decimal to fraction conversion
Converting a decimal to a fraction is a fundamental skill in mathematics. It's important for understanding numbers better and making calculations easier.
To convert a decimal to a fraction, follow these steps:
  • Identify the Decimal: Recognize the decimal number you want to convert.
  • Write as a Fraction: For decimals less than 1, simply place the decimal part over a corresponding power of ten. For example, 0.7 becomes \(\frac{7}{10}\).
  • Simplify if needed: Always reduce the fraction to its simplest form. In our example, \(\frac{7}{10}\) is already simplified.
This method helps in converting any decimal to a neat fraction, making calculations and comparisons more straightforward.
mixed numbers
A mixed number consists of a whole number and a fraction, making it a bit more complex but not too difficult to understand.
To convert a decimal greater than 1 to a mixed number, here鈥檚 the process:
  • Break Down the Decimal: Split the decimal into its whole number and fractional parts. For instance, 15.7 becomes 15 and 0.7.
  • Convert the Fractional Part: Change the fractional part to a fraction. Here, 0.7 becomes \(\frac{7}{10}\).
  • Combine the Parts: Finally, bring together the whole number and the fraction, resulting in the mixed number. So, 15.7 becomes 15 \(\frac{7}{10}\).
Understanding mixed numbers makes it easier to work with quantities that are not whole but still simple to manage.
fractions
Fractions represent a part of a whole and are a crucial concept in math.
A fraction has two parts: a numerator and a denominator. The numerator (top number) signifies how many parts are being considered, while the denominator (bottom number) shows into how many parts the whole is divided.
  • Types of Fractions: Proper fractions have numerators smaller than denominators (e.g., \(\frac{3}{4}\)). Improper fractions have numerators larger than or equal to denominators (e.g., \(\frac{9}{4}\)).
  • Conversions: Any decimal or mixed number can be converted into a fraction. Even percentages can be turned into fractions by placing the percentage over 100 and simplifying.
  • Operations: Fractions are essential in various operations, including addition, subtraction, multiplication, and division.
Mastering fractions provides a strong foundation for more advanced mathematical topics and everyday problem-solving.

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