Rounding and Estimating Numbers

If you round 6245 to the nearest thousand, you look at the hundreds digit, which is 2. Since 2 is less than 5, you round down. Therefore, 6245 rounded to the nearest thousand is 6000.

To round 16.107 to the nearest hundredth, you look at the third decimal place, which is 7. Since 7 is greater than 5, you round the second decimal place (0) up by one. Therefore, 16.107 rounded to the nearest hundredth is 16.11.

The number 58605 is nearest to the thousand 59000. When rounding to the nearest thousand, you look at the hundreds digit, which is 6 in this case. Since 6 is 5 or greater, you round up to 59000.

To round 4397 to the nearest ten, you look at the digit in the ones place, which is 7. Since 7 is 5 or greater, you round up the tens place digit (9) by one. Therefore, 4397 rounded to the nearest ten is 4400.

18000

5882

190

Rounding involves adjusting a number to a nearby value that is easier to work with, typically to a specific place value, such as rounding 47 to 50. Compatible numbers, on the other hand, are numbers that are chosen to make mental calculations easier and are often used in estimation; for example, using 50 and 20 instead of 47 and 19. While rounding aims for simplicity by reducing specificity, compatible numbers focus on creating numbers that are easy to manipulate in calculations. Both techniques are useful for estimation but serve different purposes in simplifying numbers.

To round 78060 to the nearest thousand, we look at the hundreds digit, which is 0. Since it is less than 5, we round down. Therefore, 78060 rounded to the nearest thousand is 78000.

To round 286 to the nearest ten, you look at the digit in the ones place, which is 6. Since 6 is 5 or greater, you round up the digit in the tens place (8) by one, making it 9. Therefore, 286 rounded to the nearest ten is 290.

To round 3.7 to the nearest whole number, you look at the digit in the tenths place, which is 7. Since 7 is greater than or equal to 5, you round up. Therefore, 3.7 rounded to the nearest whole number is 4.

0.93 rounded to the nearest whole number is 1. If rounding to one decimal place, it remains 0.9. If rounding to two decimal places, it stays as 0.93.

Throwing a stone at a target with one eye closed can significantly affect accuracy due to the loss of depth perception and peripheral vision. As the distance to the target increases, the challenge of estimating the distance and trajectory becomes greater, leading to reduced accuracy. Research suggests that aiming with one eye can decrease performance, especially beyond short distances, as spatial judgment relies heavily on binocular vision. Overall, accuracy diminishes as the distance increases and the limitations of monocular vision become more pronounced.

To round 7856.427 to the nearest hundred, look at the tens digit, which is 5. Since 5 or greater means you round up, you would round 7856 up to 7900. Therefore, 7856.427 rounded to the nearest hundred is 7900.

To round 248,739 to the nearest hundred, look at the digit in the tens place, which is 3. Since 3 is less than 5, you round down, keeping the hundreds digit the same. Therefore, 248,739 rounded to the nearest hundred is 248,700.

To estimate (\sqrt{5}) to the nearest hundredth, you can find two perfect squares between which 5 lies. Since (2^2 = 4) and (3^2 = 9), it follows that (\sqrt{5}) is between 2 and 3. A more precise approximation can be obtained by calculating or using a calculator, yielding (\sqrt{5} \approx 2.24). Thus, to the nearest hundredth, (\sqrt{5} \approx 2.24).

The nearest hundred to 3,570,954 is 3,570,900. To find this, you look at the last two digits (54); since 54 is closer to 00 than to 100, you round down to 3,570,900.

To round 925,913 to the millions place, you look at the hundred-thousands place, which is 9. Since it is 5 or greater, you round up. Therefore, 925,913 rounded to the millions place is 1,000,000.

To round the number 123,834,392 to the nearest thousand, you look at the digit in the hundreds place, which is 3. Since 3 is less than 5, you round down, keeping the thousands digit (4) the same. Therefore, 123,834,392 rounded to the nearest thousand is 123,834,000.

Estimating a sum or difference is useful in situations where quick decision-making is required, such as budgeting or shopping, where knowing approximate totals can help determine affordability. It is also beneficial in mental math scenarios, like gauging distances or travel times, allowing for efficient planning without needing precise calculations. Additionally, in fields like project management, estimating can help assess resource allocation and timelines without getting bogged down in exact figures.

The number 12345 rounded to the nearest ten is 12350, since the digit in the ones place (5) rounds up the tens place. If rounded to the nearest hundred, it becomes 12300, as the digit in the tens place (4) does not prompt an increase. Similarly, rounded to the nearest thousand, it is 12000.

A number that rounds to 8500, when rounded to the nearest hundred, is any number from 8450 to 8549. For example, 8467 would round to 8500 because it is closer to 8500 than to 8400. Similarly, 8533 would also round to 8500 for the same reason.

860

When rounding 0.00056 to the nearest liter, you consider the value in terms of liters. Since 0.00056 is much less than 0.5, it rounds down to 0 liters. Therefore, 0.00056 rounded to the nearest liter is 0 liters.

To round 33.54296 to the ten thousandths place, we look at the fifth decimal place, which is 6. Since 6 is greater than or equal to 5, we round up the fourth decimal place (2) by one. Therefore, 33.54296 rounded to the ten thousandths place is 33.5430.