write the following decimals as fraction in their lowest form 8.25
The correct answer and explanation is:
Sure! Let’s convert the decimal 8.25 into a fraction in its lowest terms.
Step 1: Write the decimal as a fraction
8.25 means 8 and 25 hundredths, so we can write it as: 8.25=8+0.25=8+251008.25 = 8 + 0.25 = 8 + \frac{25}{100}
Step 2: Simplify the fractional part
The fraction 25100\frac{25}{100} can be simplified by dividing numerator and denominator by their greatest common divisor (GCD), which is 25: 25100=25÷25100÷25=14\frac{25}{100} = \frac{25 \div 25}{100 \div 25} = \frac{1}{4}
Step 3: Combine the whole number and fraction
Now we have: 8+14=8×44+14=324+14=3348 + \frac{1}{4} = \frac{8 \times 4}{4} + \frac{1}{4} = \frac{32}{4} + \frac{1}{4} = \frac{33}{4}
Step 4: Final fraction
So, the decimal 8.25 is equivalent to the fraction: 334\boxed{\frac{33}{4}}
Explanation in detail (300 words)
Decimals can be converted into fractions by understanding their place value. The number 8.25 means eight whole units plus twenty-five hundredths. When written as a fraction, the decimal part, 0.25, represents twenty-five over one hundred (because the two digits after the decimal represent hundredths).
First, you write 8.25 as the sum of 8 (whole number) and 0.25 (fractional part). The decimal 0.25 equals 25100\frac{25}{100}. To simplify this fraction, you find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 25 and 100 is 25. Dividing both the numerator and denominator by 25 gives 14\frac{1}{4}.
After simplification, the fraction part of 8.25 becomes 14\frac{1}{4}. Since 8 is a whole number, you convert it into a fraction with the same denominator to add it to 14\frac{1}{4}. The whole number 8 can be expressed as 324\frac{32}{4} because 8=8×44=3248 = \frac{8 \times 4}{4} = \frac{32}{4}.
Adding 324\frac{32}{4} and 14\frac{1}{4} results in 334\frac{33}{4}. This is an improper fraction (numerator larger than denominator), but it is perfectly acceptable as a fraction form. If needed, it can be converted back to a mixed number: 8148 \frac{1}{4}.
The fraction 334\frac{33}{4} is in the lowest terms because 33 and 4 have no common divisors other than 1. This conversion shows the relationship between decimals and fractions, illustrating how decimals are just another way to express fractional values. Understanding this process helps in math subjects like algebra, measurement, and more.