209 divided by 3 estimate
The Correct Answer and Explanation is :
To estimate the result of dividing 209 by 3, let’s follow these steps:
- Estimation:
Start by rounding 209 to a nearby, simpler number that’s easier to divide by 3. In this case, 209 can be rounded to 210, which is a multiple of 3. Now, divide 210 by 3. [
210 \div 3 = 70
] So, we can estimate that 209 divided by 3 is approximately 70. - Exact Calculation:
Now, let’s calculate the exact answer for 209 divided by 3. We perform long division:
- 3 goes into 20 a total of 6 times (because 3 × 6 = 18).
- Subtract 18 from 20 to get a remainder of 2.
- Bring down the 9, making the number 29.
- 3 goes into 29 a total of 9 times (because 3 × 9 = 27).
- Subtract 27 from 29 to get a remainder of 2. Therefore, the exact result is: [
209 \div 3 = 69 \text{ remainder } 2
] Or as a decimal: [
209 \div 3 = 69.6667 \quad (\text{repeating})
]
- Explanation of Estimation:
Estimating involves rounding numbers to simplify the division process. Here, we rounded 209 to 210 to make the division easier. Since 210 is divisible by 3 without a remainder, it’s a straightforward estimate. While the exact answer (69.6667) is slightly lower, the estimation (70) provides a reasonable approximation for many practical purposes. Estimation is useful in situations where an exact answer is not necessary, such as when you’re trying to quickly assess whether a value is close to a certain range or to check the reasonableness of an answer. In this case, using 70 as an estimate gives a good approximation of the result without needing to perform long division or use a calculator.