Problem 1
Question
For exercises 1-12, rewrite the decimal number as a fraction. Simplify the fraction to lowest terms. $$ 0.7 $$
Step-by-Step Solution
Verified Answer
0.7 = \(\frac{7}{10}\)
1Step 1: Write the Decimal as a Fraction
To convert a decimal number to a fraction, first write down the decimal number divided by 1. Therefore, write 0.7 as \(\frac{0.7}{1}\).
2Step 2: Eliminate the Decimal Point
Multiply both the numerator and the denominator by 10 for each number after the decimal point to eliminate the decimal. Since 0.7 has one decimal place, multiply both by 10: \(\frac{0.7 \times 10}{1 \times 10} = \frac{7}{10}\).
3Step 3: Simplify the Fraction
The fraction \(\frac{7}{10}\) is already in its simplest form because 7 and 10 have no common factors other than 1. Therefore, \(\frac{7}{10}\) is the simplified form.
Key Concepts
decimal to fraction conversionsimplifying fractionselementary algebra
decimal to fraction conversion
Converting a decimal to a fraction might seem tricky at first, but it's really straightforward once you understand the process. Let's break it down step by step.
First, write the decimal number divided by 1. For example, if you have the decimal 0.7, you write it as \( \frac{0.7}{1} \).
Next, you need to get rid of the decimal point. To do that, you multiply both the numerator and the denominator by 10 for every number after the decimal point. Since 0.7 has one decimal place, you multiply both by 10:
\( \frac{0.7 \times 10}{1 \times 10} = \frac{7}{10} \).
Now the decimal has been converted into a fraction!
First, write the decimal number divided by 1. For example, if you have the decimal 0.7, you write it as \( \frac{0.7}{1} \).
Next, you need to get rid of the decimal point. To do that, you multiply both the numerator and the denominator by 10 for every number after the decimal point. Since 0.7 has one decimal place, you multiply both by 10:
\( \frac{0.7 \times 10}{1 \times 10} = \frac{7}{10} \).
Now the decimal has been converted into a fraction!
simplifying fractions
Once you've converted the decimal to a fraction, the next step is to simplify the fraction if needed. Simplifying a fraction means reducing it to its lowest terms so that the numerator and denominator have no common factors other than 1.
In our example, we converted 0.7 to \( \frac{7}{10} \). To check if it is in simplest form, we need to find the greatest common divisor (GCD) of 7 and 10. Since 7 is a prime number and doesn't divide evenly into 10, \( \frac{7}{10} \) is already in its simplest form.
Here's what you can do to simplify any fraction:
In our example, we converted 0.7 to \( \frac{7}{10} \). To check if it is in simplest form, we need to find the greatest common divisor (GCD) of 7 and 10. Since 7 is a prime number and doesn't divide evenly into 10, \( \frac{7}{10} \) is already in its simplest form.
Here's what you can do to simplify any fraction:
- Find the GCD of the numerator and the denominator.
- Divide both the numerator and the denominator by the GCD.
elementary algebra
Understanding decimal to fraction conversion and fraction simplification involves elementary algebra concepts. Here are some relevant ideas:
First, recognizing decimals and fractions as different representations of the same value. This is important in many areas of math and real-world applications. Second, working with numerators and denominators, especially understanding how to manipulate them by multiplication and division.
Elementary algebra also involves the concept of greatest common divisors (GCD), which helps in simplifying fractions.
Key points include:
First, recognizing decimals and fractions as different representations of the same value. This is important in many areas of math and real-world applications. Second, working with numerators and denominators, especially understanding how to manipulate them by multiplication and division.
Elementary algebra also involves the concept of greatest common divisors (GCD), which helps in simplifying fractions.
Key points include:
- Understanding place value in decimals.
- Basics of multiplication and division with whole numbers and decimals.
- Concepts of prime numbers and greatest common divisors.