Convert 2/3 to a decimal. Round to the nearest hundredth.
The Correct Answer and Explanation is :
To convert the fraction ( \frac{2}{3} ) into a decimal, we can perform the division of the numerator by the denominator.
- Division Process: We take 2 (the numerator) and divide it by 3 (the denominator). Since 2 is smaller than 3, we know the result will be less than 1. To proceed with the division, we can express 2 as 2.000 to allow for decimal places.
- First Division: 3 goes into 20 six times (since ( 3 \times 6 = 18 )). This gives us a remainder of 2 (20 – 18 = 2). We write down 0.6.
- Second Division: Bring down another 0, making it 20 again. As before, 3 goes into 20 six times, giving a remainder of 2. We can see this is going to repeat.
- This process continues indefinitely, producing a recurring decimal: ( 0.666…).
- Rounding: Since we need to round to the nearest hundredth, we look at the third decimal place to determine how to round the second decimal place. The decimal ( 0.666… ) can be written as ( 0.67 ) when rounded to the nearest hundredth. The third decimal place is a 6, which is 5 or more, prompting us to round up.
- Final Result: Therefore, the decimal equivalent of ( \frac{2}{3} ), rounded to the nearest hundredth, is ( 0.67 ).
Summary:
- Conversion Method: Division (2 ÷ 3 = 0.666…)
- Rounding: Based on the third decimal place.
- Final Answer: ( 0.67 )
This process illustrates the connection between fractions and their decimal representations, providing an essential skill in mathematics. Understanding how to convert and round decimal numbers is vital for various applications in both everyday life and more advanced mathematical contexts.