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Chapter 5: Problem 6

Write each decimal as a fraction or mixed number in simplest form. $$6.35$$

Short Answer

Expert verified
6.35 as a mixed number is \(6\frac{7}{20}\).

Step by step solution

01

Identify the Whole Number

The decimal number given is 6.35. Note that 6 is the whole number part of the decimal.
02

Express the Decimal Part as a Fraction

The decimal part is 0.35. We can express 0.35 as a fraction. Since there are two digits after the decimal, we place 35 over 100, giving us \(\frac{35}{100}\).
03

Simplify the Fraction

Simplify \(\frac{35}{100}\) by finding the greatest common divisor (GCD) of 35 and 100. The GCD is 5. Divide both the numerator and the denominator by 5 to simplify: \(\frac{35 \div 5}{100 \div 5} = \frac{7}{20}\).
04

Combine the Whole Number and Fraction

Combine the whole number 6 and the simplified fraction \(\frac{7}{20}\). Thus, the mixed number representation of 6.35 is \(6\frac{7}{20}\).

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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 into a fraction is a useful skill that helps in understanding relationships between different types of numbers. Let's dive into how to convert a decimal like 0.35 into a fraction step-by-step.

Begin with writing down the decimal divided by 1:
  • For example, 0.35 can be written as \( \frac{0.35}{1} \).
Next, identify how many digits are present after the decimal point:
  • 0.35 has two digits, so we multiply both the numerator and the denominator by 100 (since 10 raised to the power of the number of digits, 2, is 100).
  • This gives us \( \frac{35}{100} \).
You've now converted the decimal into a fraction. The next step would be to further simplify this fraction, which we'll explore in another section.
Mixed Numbers
Understanding mixed numbers is key to dealing with compositions of whole numbers and fractions. A mixed number is made up of a whole number and a proper fraction.

Let's look at how you can transform a decimal like 6.35 into a mixed number:
  • First, identify the whole number part of the decimal. In 6.35, the whole number is 6.
  • Then express the remaining decimal part, 0.35, as a fraction.
  • Once you have the fraction form of the decimal, you combine it with the whole number.
  • For our example, it becomes \( 6\frac{35}{100} \) which can be simplified further, as we'll explain in the next section, to \( 6\frac{7}{20} \).
This final form, \( 6\frac{7}{20} \), is the simplest mixed number equivalent of the decimal 6.35.
Simplifying Fractions
Simplifying fractions is all about making them as simple as possible, which means finding the smallest possible numbers that can express the same value. Here's how to simplify a fraction like \( \frac{35}{100} \):

  • First, find the greatest common divisor (GCD) for both the numerator (35) and the denominator (100).
  • The GCD is the largest number that evenly divides both numbers.
  • For 35 and 100, the GCD is 5.
Divide both the numerator and the denominator by the GCD:
  • \( \frac{35 \div 5}{100 \div 5} = \frac{7}{20} \).
This process ensures that you have the simplest form of the fraction, which in this example becomes \( \frac{7}{20} \). Keeping fractions simple makes calculations and comparisons much easier.

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Most popular questions from this chapter

Order the fractions from least to greatest. $$\frac{5}{12}, \frac{3}{4}, \frac{1}{3}, \frac{5}{6}$$

Order the fractions from least to greatest. $$-\frac{23}{30},-\frac{4}{5},-\frac{2}{3},-\frac{7}{10}$$

Find the distance between each pair of points. Round to the nearest tenth, if necessary. $$Q\left(5 \frac{1}{4}, 3\right), R\left(2,6 \frac{1}{2}\right)$$

Show that \(0.999 \ldots=1\)

Express each number in scientific notation. A human blinks about 6.25 million times a year.
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