Write 175% as a decimal and as a fraction in simplest form.
The correct answer and explanation is:
Sure! Let’s start with the answer and then I’ll explain the steps clearly.
Answer:
- 175% as a decimal: 1.75
- 175% as a fraction in simplest form: 74\frac{7}{4}
Explanation:
Step 1: Understanding percent
The symbol “%” means “per hundred.” So, 175% literally means “175 per 100” or 175100\frac{175}{100}.
Step 2: Convert percent to decimal
To convert a percentage to a decimal, divide the number by 100: 175%=175100=1.75175\% = \frac{175}{100} = 1.75
This means 175% as a decimal is 1.75.
Step 3: Convert percent to fraction
We already wrote 175% as 175100\frac{175}{100}. Now, simplify the fraction:
- Find the greatest common divisor (GCD) of 175 and 100.
- Factors of 175: 1, 5, 7, 25, 35, 175
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The greatest common factor they share is 25.
- Divide numerator and denominator by 25:
175÷25100÷25=74\frac{175 \div 25}{100 \div 25} = \frac{7}{4}
So, 175% as a fraction in simplest form is 74\frac{7}{4}.
Step 4: Interpretation
- As a decimal, 1.75 means one whole plus 0.75 (which is 3/4).
- As a fraction, 74\frac{7}{4} means 7 parts out of 4, or 1 and 3/4.
Summary:
- To convert from percent to decimal, divide by 100.
- To convert from percent to fraction, write as numerator over 100, then simplify.
This process helps in many math and real-life problems like calculating discounts, interest rates, or proportions, where percentages are frequently converted into decimals or fractions for calculations