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Chapter 9: Problem 97

Write each decimal as a fraction and each fraction as a decimal. 0.21

Short Answer

Expert verified
0.21 is \( \frac{21}{100} \).

Step by step solution

01

Understand the Decimal

The decimal given is 0.21. To convert it into a fraction, we need to recognize the place value of each digit. In 0.21, 2 is in the tenths position and 1 is in the hundredths position.
02

Write the Decimal as a Fraction

0.21 can be expressed as \( \frac{21}{100} \). This is because the two digits after the decimal point indicate hundredths.
03

Simplify the Fraction

Check if the fraction \( \frac{21}{100} \) can be simplified. Since 21 and 100 do not have any common factors besides 1, \( \frac{21}{100} \) is already in its simplest form.
04

Write the Fraction as a Decimal

To ensure accuracy, converting back, \( \frac{21}{100} \) as a decimal is 0.21, confirming the conversion is correct.

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Key Concepts

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

Understanding Place Value in Decimals
When working with decimals, the concept of place value is crucial. Each digit in a decimal number has a specific place value, depending on its position relative to the decimal point. For example, in the decimal 0.21:
  • The digit 2 is in the tenths place, which means it represents 2 tenths or 0.2.
  • The digit 1 is in the hundredths place, representing 1 hundredth or 0.01.
Recognizing place value helps to convert decimals into fractions easily. By understanding that 0.21 has two digits after the decimal point, we identify it as a fractional value in terms of hundredths.
Simplifying Fractions
Fraction simplification, or reducing a fraction to its simplest form, involves finding the greatest common divisor (GCD) of the numerator and denominator. A fraction is simplified when the only common factor between the numerator and denominator is 1.In our example with the fraction \( \frac{21}{100} \):
  • We check if both 21 and 100 have any common factors other than 1.
  • Since they don鈥檛 share any factors other than 1, \( \frac{21}{100} \) is already in its simplest form.
Simplifying fractions makes them easier to read and often more intuitive to work with in mathematical problems.
Converting Fractions to Decimals
Converting a fraction to a decimal involves division. You divide the numerator by the denominator. This process changes the fraction into a different form while retaining its value.Taking the fraction \( \frac{21}{100} \) from our example:
  • You divide 21 by 100.
  • This gives you a decimal answer of 0.21.
This conversion is useful because decimals can sometimes be more straightforward to comprehend and use in calculations, especially in everyday applications like measuring or finances.

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