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Chapter 2: Problem 120

Convert the decimal to a fraction. $$3.4$$

Short Answer

Expert verified
The decimal number 3.4 can be written as the mixed fraction \(3 \frac{2}{5}\).

Step by step solution

01

Understanding the Decimal Place Value

The decimal number 3.4 can be viewed as the integer '3' and the fraction '4' out of 10 (since '4' is in the tenths place). Hence, the decimal number can be rewritten as \(3 + \frac{4}{10}\).
02

Mixing the Fraction

Next, the mix number will be converted into a decimal. Consider '3' as your whole number and \(\frac{4}{10}\) as your fraction. This can be written as \(3 \frac{4}{10}\).
03

Simplification

The fraction component \(\frac{4}{10}\) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (in this case, '2'). This yields \(\frac{2}{5}\). Then, rewrite the entire number using this simplified fraction, resulting in \(3 \frac{2}{5}\).

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Key Concepts

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

Decimal Place Value
Understanding decimal place value is the first step in converting a decimal to a fraction. Each digit in a decimal has a specific place value that indicates its weight. For example, in the number 3.4, the digit '3' is in the ones place, representing three whole units. The digit '4' is in the tenths place, representing four parts out of ten.

By recognizing that 4 is in the tenths place, we can translate the decimal 3.4 into a sum: 3 whole units plus four-tenths. This can be expressed as a combination of a whole number and a fractional part, which we will discuss in the next sections.

When breaking down decimals, remember:
  • The first digit to the right of the decimal point is in the tenths place.
  • The second digit is in the hundredths place.
  • And so on, for thousandths, ten-thousandths, etc.
Mixed Numbers
Mixed numbers are numbers that consist of an integer and a fraction. When converting decimals to fractions, recognizing mixed numbers is vital. In our exercise, we took the decimal 3.4 and initially represented it as 3 plus \(\frac{4}{10}\).

The number 3 represents the whole number part, while \(\frac{4}{10}\) is the fractional part. This combined form is what is known as a mixed number, expressed as \(3 \frac{4}{10}\).

Mixed numbers can simplify complex decimal readings by clearly showing the separation between whole units and fractional components, aiding in better comprehension and conversion processes.
Simplifying Fractions
Simplifying fractions is an essential skill in converting decimals to fractions efficiently. A fraction is simplified when its numerator and denominator have no common factors other than one.

In our example, the fraction \(\frac{4}{10}\) needed simplification. Both the numerator '4' and the denominator '10' can be divided by 2, which is their greatest common divisor. By dividing both by 2, \(\frac{4}{10}\) simplifies to \(\frac{2}{5}\).

Remember these steps to simplify:
  • Identify the greatest common divisor of the numerator and denominator.
  • Divide both the numerator and denominator by this number.
Simplifying fractions makes them easier to understand, use, and compare. It also ensures that any numeric value expressed as a fraction represents the simplest form possible.

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Most popular questions from this chapter

Four hundred empty soft drink cans weigh 18.75 Ib. A recycling center pays \(\$ .75\) per pound for cans. Find the amount received for the 400 cans. Round to the nearest cent.

Convert the decimal to a fraction. $$4.55$$

What is the largest fraction with a denominator of 5 that is less than \(0.78 ?\)

You had a balance of \(\$ 347.08\) in your checking account. You then made a deposit of \(\$ 189.53\) and wrote a check for \(\$ 62.89 .\) Find the new balance in your checking account.

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{10}{11} \quad 0.909$$
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