Question

Write 2.09 as a mixed number. Let (x) be equal to the repeating decimal. The decimal has 2 repeating digits, so multiply each side of the equation by 10^2 or 100.

Answer 1

To write 2.09 as a mixed number, divide the numerator and denominator of the decimal fraction by a power of 10, and write the resulting fraction as a mixed number.

Step-by-step explanation:

To write 2.09 as a mixed number, we first need to understand what a mixed number is. A mixed number consists of a whole number part and a fractional part. To convert a decimal to a mixed number, we can look at the digits after the decimal point. In this case, there are two digits after the decimal point, so the fractional part will have two digits.

To convert the decimal to a fraction, we multiply both the numerator and denominator by 10 raised to the power of the number of decimal places. In this case, we multiply both the numerator and denominator by 10^2, which is 100. This gives us:

2.09 = 209/100

Now we can write it as a mixed number by dividing the numerator (209) by the denominator (100) to get the whole number part and the fractional part.

209 ÷ 100 = 2 R 9

So the mixed number representation of 2.09 is 2 and 9/100.