Write 0.009 as a fraction.
The correct answer and explanation is:
The decimal 0.009 can be written as a fraction by following these steps:
Step 1: Understand the place value of the decimal.
The decimal 0.009 has three digits after the decimal point. The last digit, 9, is in the thousandths place. This means 0.009 is nine thousandths.
Step 2: Write the decimal as a fraction with the denominator based on the place value.
Since the decimal ends in the thousandths place, write it as:
91000\frac{9}{1000}
Step 3: Simplify the fraction if possible.
The numerator is 9 and the denominator is 1000. The greatest common divisor (GCD) of 9 and 1000 is 1 because 9 factors into 3 × 3 and 1000 factors into 2³ × 5³, so they share no common factors other than 1.
Because the GCD is 1, the fraction 91000\frac{9}{1000} is already in its simplest form.
Final answer:
0.009=910000.009 = \frac{9}{1000}
Explanation:
Decimals represent parts of a whole number, based on powers of ten. When converting a decimal to a fraction, the key step is to identify which place value the decimal reaches. For example, 0.1 is one-tenth, 0.01 is one-hundredth, and 0.009 is nine-thousandths because the digit 9 is in the third place after the decimal.
Once the place value is identified, the decimal can be expressed as the numerator (the digits without the decimal point) over the denominator (which is 1 followed by as many zeros as the number of decimal places). Here, since the decimal has three places, the denominator is 1000.
Simplification involves finding the greatest common divisor (GCD) between numerator and denominator and dividing both by it. In this case, 9 and 1000 do not share any common factors other than 1, so the fraction is already in its simplest form.
This method works for any terminating decimal, and understanding this process helps in converting decimals to fractions quickly and accurately.