Problem 4 Convert the percent to a decimal... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 7: Problem 4

Convert the percent to a decimal and a fraction. $$124 \%$$

Short Answer

Expert verified

124% is 1.24 as a decimal and 31/25 as a fraction.

Step by step solution

- Convert Percent to Decimal

To convert a percent to a decimal, divide the percent value by 100. For example, 124% divided by 100 is 1.24.

- Write the Decimal as a Fraction

To convert the decimal 1.24 to a fraction, first recognize that 1.24 means 1 + 0.24. Next, convert 0.24 to a fraction by considering it as 24/100, which simplifies by dividing both the numerator and the denominator by their greatest common divisor, which is 4, giving 6/25. Thus, 1.24 becomes 1 + 6/25, which can be written as an improper fraction by converting the mixed number to a single fraction: (1 * 25 + 6)/25, resulting in 31/25.

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Key Concepts

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

Percent Conversion

Converting percentages to decimals is a fundamental skill in math. It's quite straightforward: you just need to divide the percentage value by 100.
For instance, if we take the example of 124%, we can convert it to a decimal by simply performing the division:
ewline 124 梅 100 = 1.24.
This is why 124% becomes 1.24 as a decimal. Always remember, the process involves moving the decimal point two places to the left when dividing by 100.
Hence, 124% 鈫� 1.24.

Decimal to Fraction

Once you have a decimal, converting it to a fraction involves a few key steps. Let's use 1.24 as an example.
First, recognize that 1.24 can be split into two parts:
1 + 0.24.
For the decimal part, 0.24, we express it as a fraction of 100:
0.24 = 24/100.
Next, simplify this fraction. We identify the greatest common divisor (GCD) of 24 and 100, which is 4.
Then, divide both the numerator and the denominator by the GCD:

24 梅 4 = 6
100 梅 4 = 25

Thus, 0.24 simplifies to 6/25.
Combining this with the whole number, we get:
1.24 = 1 + 6/25.
This conversion gives a clearer view of where the decimal number originates from in fractional form.

Simplifying Fractions

The final step is important: simplifying fractions. In our example, we now have the mixed number 1 + 6/25.
To convert this to an improper fraction:
first, multiply the whole number by the denominator of the fraction (which is 25).
1 脳 25 = 25.
Next, add the numerator of the fraction to this product:
25 + 6 = 31.
Now, place this result over the original denominator:
31/25.
This is your final simplified improper fraction.

Simplifying fractions ensures they are in their simplest form, making them easier to understand and work with.
This conversion ensures accuracy and better comprehension.

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91影视

Convert the percent to a decimal and a fraction. $$124 \%$$

Short Answer

Step by step solution

- Convert Percent to Decimal

- Write the Decimal as a Fraction

Key Concepts

Percent Conversion

Decimal to Fraction

Simplifying Fractions

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