Write the decimal as a fraction. 0.09
The correct answer and explanation is:
✅ Correct Answer:
The decimal 0.09 as a fraction is: 9100\frac{9}{100}
📘 300-Word Explanation:
To convert the decimal 0.09 into a fraction, follow these steps:
Step 1: Understand Place Value
The number 0.09 means 9 hundredths. The digit 9 is in the hundredths place. This is because:
- The first digit after the decimal is the tenths place (0.0), which is 0 in this case.
- The second digit is the hundredths place, which is 9.
So, we can write: 0.09=91000.09 = \frac{9}{100}
Step 2: Simplify the Fraction
Now we check if the fraction can be simplified. The numerator is 9, and the denominator is 100.
- The greatest common divisor (GCD) of 9 and 100 is 1, which means the fraction is already in its simplest form.
So, the final simplified fraction is: 9100\frac{9}{100}
🔁 Why This Works:
Decimals are just another way to express fractions with denominators that are powers of 10.
- 0.1 = 1/10 (tenths)
- 0.01 = 1/100 (hundredths)
- 0.001 = 1/1000 (thousandths)
So: 0.09=9×1100=91000.09 = 9 \times \frac{1}{100} = \frac{9}{100}
✅ Final Answer Again:
9100\boxed{\frac{9}{100}}
This method is helpful in math, finance, and science where you often need to switch between decimals and fractions for precision and clarity.