Write 7/13 as a decimal and round to the nearest hundredth
The Correct Answer and Explanation is:
To write the fraction 7/13 as a decimal, we perform the division:
7 ÷ 13 = 0.538461538…
This is a repeating decimal, which means the digits “538461” keep repeating indefinitely.
Now we round this decimal to the nearest hundredth. The hundredths place is the second digit after the decimal point. In 0.538461…, the hundredths place is 3, and the digit after it (which is in the thousandths place) is 8.
According to the rules of rounding, if the digit after the one you are rounding to is 5 or greater, you round up. Since 8 is greater than 5, we round 0.538 up to 0.54.
Final Answer:
7/13 as a decimal rounded to the nearest hundredth is 0.54.
Explanation
When converting a fraction to a decimal, the process involves dividing the numerator by the denominator. In this case, 7 is the numerator and 13 is the denominator. Performing the division 7 divided by 13 gives a decimal result of 0.538461538…, which continues repeating. This type of decimal is known as a repeating decimal, and it does not terminate or end cleanly.
To round a decimal to the nearest hundredth, we first identify the digits in the tenths and hundredths places. For the number 0.538461…, the digit in the tenths place is 5, and the digit in the hundredths place is 3. The next digit, which is in the thousandths place, is 8. This digit determines whether we round the hundredths place up or keep it the same.
The rule for rounding is simple: if the digit immediately after the place you are rounding to is 5 or higher, you increase the value in the rounding place by 1. If it is less than 5, you leave the rounding place as it is. In this example, since the thousandths digit is 8, we increase the hundredths digit (3) by 1. This gives us a rounded value of 0.54.
Understanding how to round and convert fractions into decimals is important in many real-world applications, such as dealing with money, measurements, or data analysis.
