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Chapter 2: Problem 125

Convert the decimal to a fraction. $$0.045$$

Short Answer

Expert verified
The decimal 0.045 converts to the fraction \( \frac {9}{200} \)

Step by step solution

01

Understanding Decimal Place Value

Since the given decimal 0.045 falls in the hundredths place, it will be written over 1000 when converted into a fraction.
02

Fraction Conversion

Convert the decimal to a fraction. The decimal 0.045 converts to \( \frac {45}{1000} \).
03

Fraction Simplification

The next step is to simplify the fraction. When both the numerator and denominator are divisible by the same number, in this case 5, the fraction can be simplified. After simplification, \( \frac {45}{1000} \) becomes \( \frac {9}{200} \).

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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 decimals to fractions. A decimal number has different places, each representing a power of ten. The number 0.045 can be broken down as 0 ones, 0 tenths, 4 hundredths, and 5 thousandths.
Each digit to the right of the decimal point has a specific place value:
  • The first digit is in the tenths place, which is 1/10 of a whole.
  • The second digit is in the hundredths place, which is 1/100 of a whole.
  • The third digit is in the thousandths place, which is 1/1000 of a whole.
For 0.045, the last digit "5" is in the thousandths place, meaning the whole number is equivalent to 45 over 1000.
Fraction Simplification
Fraction simplification involves reducing a fraction to its simplest form. In the fraction of 45/1000, both terms can be divided by the greatest common divisor (GCD).
The GCD of 45 and 1000 is 5, which gives:
  • Divide both the numerator and the denominator by 5:
\[ \frac{45}{1000} \to \frac{45 \div 5}{1000 \div 5} = \frac{9}{200} \]
Thus, the fraction simplifies to 9/200. By reducing fractions, we work with smaller numbers, making calculations easier and results more comprehensible.
Converting Decimals
The process of converting decimals to fractions includes several straightforward steps. First, identify the place value of the final digit. In the case of 0.045, the 5 is in the thousandths place.
Convert the decimal to a fraction using this place value, which gives us:
  • 0.045 becomes \( \frac{45}{1000} \)
Then, simplify the fraction to its smallest form, focusing on the fractions' numerator and denominator to find common divisors. This makes the fraction more efficient for use in calculations.
Mathematics Education
Teaching and learning mathematics effectively involves breaking down complex concepts into simple, easy-to-understand steps. Converting decimals to fractions is one such foundational skill.
Here are a few crucial tips:
  • Begin with a strong grasp of place value, so converting numbers becomes intuitive.
  • Practice fraction simplification to become comfortable with common divisors and fraction operations.
  • Engage in exercises regularly to build confidence and fluency in these concepts.
Mathematics education thrives on practice and understanding, paving the way for advanced math skills with a strong foundation. Encouraging inquiry and problem-solving will help students master skills like converting decimals to fractions with ease.

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Most popular questions from this chapter

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