The Correct Answer and Explanation is:
The correct answer is 22.59.
To convert the mixed number 22 59/100 into a decimal number, you can think of the mixed number as the sum of its two parts: the whole number and the fraction. In this problem, the whole number is 22, and the fraction is 59/100.
First, let’s focus on the whole number, 22. This number will be the part of our final decimal that appears to the left of the decimal point.
Next, we need to convert the fractional part, 59/100, into its decimal form. The fraction 59/100 is read as “fifty-nine hundredths.” This name directly tells us how to write it as a decimal. In the decimal system, the first place after the decimal point is the tenths place, and the second place is the hundredths place. Since our fraction is in hundredths, we can write it as 0.59. The 5 is in the tenths place, and the 9 is in the hundredths place, correctly representing 59 hundredths.
Finally, we combine the whole number part and the decimal part by adding them together. You add the whole number 22 to the decimal 0.59:
22 + 0.59 = 22.59
Another way to approach this is to convert the mixed number into an improper fraction first. To do this, you multiply the whole number (22) by the denominator (100) and then add the numerator (59).
(22 × 100) + 59 = 2200 + 59 = 2259.
This gives you the new numerator, and the denominator remains 100, so the improper fraction is 2259/100.
Now, to turn this fraction into a decimal, you divide the numerator by the denominator. Dividing 2259 by 100 simply involves moving the decimal point two places to the left, which results in 22.59. Both methods confirm that the decimal representation of 22 59/100 is 22.59.
