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Chapter 8: Problem 27

(Section 6.3) Convert 0.06 to a fraction.

Short Answer

Expert verified
0.06 converts to the fraction \( \frac{3}{50} \).

Step by step solution

01

Understanding the Position of the Decimal

To convert a decimal to a fraction, we first need to understand what each digit represents. The decimal 0.06 has a '6' in the hundredths place, meaning it represents 6 hundredths or 6 parts out of 100.
02

Writing the Decimal as a Fraction

We write the decimal 0.06 as a fraction by placing the number '6' over '100'. So, 0.06 becomes \( \frac{6}{100} \).
03

Simplifying the Fraction

Next, we simplify \( \frac{6}{100} \) by finding the greatest common divisor (GCD) of both the numerator and the denominator. The GCD of 6 and 100 is 2.
04

Dividing by the GCD

Divide both the numerator and the denominator by their GCD. \( \frac{6}{100} \div \frac{2}{2} = \frac{3}{50} \). Thus, the fraction simplifies to \( \frac{3}{50} \).
05

Presenting the Simplified Fraction

Confirm that \( \frac{3}{50} \) is in its simplest form since 3 and 50 have no common factors other than 1. The conversion is complete.

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Key Concepts

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

Simplifying Fractions
When you convert a decimal to a fraction, the task isn't finished until you simplify the fraction. Simplifying a fraction means reducing it to its simplest form where the numerator and the denominator have no common factors other than 1. For example, in the fraction \( \frac{6}{100} \), the numbers 6 and 100 share a common factor of 2, which means we can make the fraction simpler.
Consider a few steps to simplify fractions:
  • Find the greatest common divisor (GCD) of the numerator and the denominator.
  • Divide both the numerator and the denominator by the GCD.
  • Check if the resulting fraction is in its simplest form by ensuring the numerator and denominator are coprime.
Simplifying makes fractions easier to understand and work with in calculations, helping you identify equivalent and reduced forms that reveal the basic ratios.
Greatest Common Divisor
The greatest common divisor (GCD) is a key concept when simplifying fractions. It refers to the largest number that can divide both the numerator and the denominator without leaving a remainder.
To find the GCD:
  • List the factors of both numbers you are comparing.
  • Identify the largest factor common to both lists.
In our example, the GCD of 6 and 100 is 2 because 2 is the largest number that divides both 6 and 100 evenly. By using the GCD, you ensure the fraction is reduced to its smallest possible terms, which makes it easier to read and compare to other fractions. This step is crucial because fractions that might seem different can be equivalent if they are not in their simplest form.
Understanding Decimal Places
Decimals represent parts of whole numbers, and the position of a digit in a decimal number tells you its place value. For instance, in the decimal 0.06, the '6' is in the hundredths place, which indicates 6 parts out of 100.
Here's how you can understand and manage decimal places:
  • Each digit in a decimal is a fraction with a denominator that is a power of 10.
  • The first digit to the right of the decimal is the tenths place, the next is the hundredths, then thousandths, and so on.
By converting a decimal to a fraction, like 0.06 to \( \frac{6}{100} \), you translate this base-10 fraction into a form that can be simplified and compared more easily. Understanding how decimal places work is a foundation for delving into more complex mathematics.

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Most popular questions from this chapter

Estimate each value using the method of clustering. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary. $$ 81+41+92+38+88+80 $$

Estimate each value. After you have made an estimate, find the exact value. Results may vary. \((\) Section 8.2\() 7,316-2,305\)

Use the distributive property to obtain the exact result. \((\) Section 8.4) \(15 \cdot 83\)

Estimate each value using the method of rounding. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary. $$ (1.07)(13.89) $$

For problems 111-125, estimate each sum using the method of rounding fractions. After you have made an estimate, find the exact value. Compare the exact and estimated values. Results may vary. \(\frac{3}{8}+\frac{5}{6}\)
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