Express $16 / 3$ as a decimal correct to 4 decimal places.
Answer (2)
The fraction 3 16 is expressed as a decimal by dividing 16 by 3, which results in 5.3333... To round correctly to 4 decimal places, we keep it as 5.3333 since the next digit does not require rounding up. Thus, the final answer is 5.3333 .
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Divide 16 by 3 to get the decimal representation: 16/3 = 5.333333... .
Round the result to 4 decimal places.
Since the 5th decimal place is 3 (less than 5), round down.
The fraction 3 16 as a decimal correct to 4 decimal places is 5.3333 .
Explanation
Understanding the Problem We are asked to express the fraction 3 16 as a decimal correct to 4 decimal places. This means we need to perform the division and then round the result to the specified number of decimal places.
Performing the Division To express 3 16 as a decimal, we perform the division 16 ÷ 3 . The result of this division is 5.3333333... where the digit 3 repeats indefinitely.
Rounding to 4 Decimal Places Now, we need to round the decimal 5.3333333... to 4 decimal places. To do this, we look at the 5th decimal place. If it is 5 or greater, we round up the 4th decimal place. If it is less than 5, we leave the 4th decimal place as it is. In this case, the decimal is 5.3333333... , so the 5th decimal place is 3, which is less than 5. Therefore, we round down and keep the 4th decimal place as it is.
Final Result Rounding 5.3333333... to 4 decimal places gives us 5.3333 .
Final Answer Therefore, 3 16 expressed as a decimal correct to 4 decimal places is 5.3333 .
Examples
In practical situations, you might need to convert a fraction to a decimal when dealing with measurements or quantities that are more easily understood in decimal form. For example, if you have 16 slices of a pie to be divided equally among 3 people, each person would get 3 16 slices. Converting this to a decimal (approximately 5.3333) allows for easier visualization and distribution of the pie slices. This conversion is also useful in financial calculations, where amounts are often expressed in decimal form for precise accounting.
