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Chapter 5: Problem 14

Write each fraction or mixed number as a decimal. $$\frac{4}{25}$$

Short Answer

Expert verified
0.16

Step by step solution

01

- Understand the problem

The goal is to convert the fraction \(\frac{4}{25}\) into a decimal. This involves division of the numerator (4) by the denominator (25).
02

- Perform the Division

To convert \(\frac{4}{25}\) to a decimal, divide 4 by 25. \[ 4 \div 25 = 0.16 \]

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Key Concepts

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

fractions
A fraction represents a part of a whole. It consists of two numbers: a numerator and a denominator. The numerator (top number) indicates how many parts we have, and the denominator (bottom number) shows how many equal parts the whole is divided into. For example, in the fraction \(\frac{4}{25}\), '4' is the numerator and '25' is the denominator.
  • Fractions are often used to denote quantities less than one.
  • They can also represent division statements, which will make converting them to decimals easier.
  • Mixed numbers are composed of both whole numbers and fractional parts.
Understanding fractions is crucial for converting them into decimals because it highlights the part-to-whole relationship.
decimals
Decimals are another way to represent fractions. They use a decimal point to divide the whole number part from the fractional part.
  • In our example, the fraction \(\frac{4}{25}\) converts to the decimal '0.16'.
  • The decimal point helps show place value, i.e., tenths, hundredths, thousandths, etc.
  • Unlike fractions, decimals are based on powers of 10, making them easier to interpret and manipulate, especially in calculations.
For instance, the decimal '0.75' corresponds to the fraction \(\frac{75}{100}\), or simplified, \(\frac{3}{4}\). This shows that decimals and fractions are just different forms of the same concept.
division
Division is a core mathematical operation important for converting fractions to decimals.
  • Converting the fraction \(\frac{4}{25}\) to a decimal requires dividing 4 (numerator) by 25 (denominator).
  • This process can be visualized as distributing 4 equally among 25 parts.
  • Performing the division \[ 4 \div 25 = 0.16 \] results in the decimal '0.16'.
This was achieved by extending the division to two decimal places, as 25 goes into 400 sixteen times. Understanding division helps to easily convert fractions to decimals and vice versa.

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Most popular questions from this chapter

The prices of 10 single-family, three-bedroom homes for sale in Boston, Massachusetts, are listed for a recent year. Find the mean, median, and mode (if one exists).$$\begin{aligned}&\$ 300,000, \$ 2,495,000, \$ 2,120,000, \$ 220,000\\\&\$ 194,000, \$ 391,000, \quad \$ 315,000, \quad \$ 330,000\\\ &\$ 435,000, \$ 250,000\end{aligned}$$

For Exercises \(71-82,\) simplify by using the order of operations. $$15.06-1.92-0.4^{2}$$

Certain DVD titles are on sale for 2 for \(\$ 32\). If they regularly sell for \(\$ 19.99,\) how much can a person save by buying 4 DVDs?

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For Exercises \(59-66,\) simplify the expressions. $$(0.1)^{3}$$
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