what is the simplified fraction is equal to 0.53 ?
The correct answer and explanation is:
The decimal 0.53 can be expressed as a simplified fraction. Here’s how you do it step-by-step:
Step 1: Write 0.53 as a fraction
0.53 means 53 hundredths, so: 0.53=531000.53 = \frac{53}{100}
Step 2: Simplify the fraction if possible
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.
- Numerator = 53
- Denominator = 100
Now, check if 53 and 100 share any common factors other than 1.
- 53 is a prime number, so its only factors are 1 and 53.
- 100 factors include 1, 2, 4, 5, 10, 20, 25, 50, 100.
Since 53 is prime and does not divide evenly into 100, the GCD of 53 and 100 is 1.
Step 3: Final simplified fraction
Since the GCD is 1, the fraction 53100\frac{53}{100} is already in its simplest form.
Answer:
0.53=531000.53 = \frac{53}{100}
Explanation:
Decimals are often easier to express as fractions by identifying the place value. Here, 0.53 is two decimal places, meaning it represents “53 hundredths.” This is why we write it as 53100\frac{53}{100}.
After writing the decimal as a fraction, simplifying it involves checking for common factors between numerator and denominator. The prime nature of 53 makes it less likely to simplify further when paired with 100, which is composed of factors 2 and 5. Since no common factors exist, the fraction is already in the simplest form.
This conversion from decimal to fraction is useful in many mathematical contexts, such as when adding, subtracting, or comparing numbers, because working with fractions can sometimes be clearer or necessary depending on the problem.
If you want to convert other decimals to fractions or simplify more complex decimals, the same process applies: write the decimal as a fraction with a power of 10 denominator (10, 100, 1000, etc.), then reduce by the greatest common divisor.