Question

round to the nearest hundred.
8942

8942 rounded to the nearest hundred is \boxed{}

Explanation:

Step1: Identify the hundreds place

In 8942, the digit in the hundreds place is 9 (since 8942 = 8*1000 + 9*100 + 4*10 + 2*1). The digit to the right of the hundreds place (the tens place) is 4.

Step2: Apply rounding rule

The rounding rule for the nearest hundred is: if the tens digit is 5 or more, we round up the hundreds digit; if it's less than 5, we keep the hundreds digit the same and set the tens and ones digits to 0. Here, the tens digit is 4 (less than 5), but wait, wait—wait, actually, 8942: let's re - check. Wait, 8942, the hundreds place is 9, tens is 4, ones is 2. Wait, no, wait: 8 (thousands), 9 (hundreds), 4 (tens), 2 (ones). Wait, but when rounding to the nearest hundred, we look at the tens digit. But 942 is the last three digits? Wait, no, 8942: the number is 8 thousands, 9 hundreds, 4 tens, 2 ones. To round to the nearest hundred, we consider the number formed by the hundreds, tens, and ones digits, which is 942. Wait, no, the correct way is: the hundreds digit is 9, the digit to the right (tens place) is 4. But wait, if we have 8942, and we round to the nearest hundred, we look at the tens digit. But 942: when rounding 942 to the nearest hundred, since the tens digit is 4 (less than 5), we would round 942 to 900? But wait, 8942 is 8000 + 942. Wait, no, that's a mistake. Wait, no: 8942, the hundreds place is 9, the tens place is 4. Wait, but actually, when the hundreds digit is 9 and we round up, but wait, no—wait, let's do it properly. The number is 8942. To round to the nearest hundred, we look at the digit in the tens place (4) and the digit in the hundreds place (9). Wait, the rule is: for rounding to the nearest hundred, we look at the tens digit. If the tens digit is ≥5, we add 1 to the hundreds digit; if <5, we leave the hundreds digit as is, and set the tens and ones digits to 0. But in this case, the hundreds digit is 9, and the tens digit is 4. But wait, 8942: let's think of it as between 8900 and 9000. Wait, 8942 is 42 more than 8900 and 58 less than 9000? Wait, no, 9000 - 8942 = 58, 8942 - 8900 = 42. Wait, but that's not the right way. Wait, no, the correct method is: the hundreds place is 9, tens is 4. But when the hundreds digit is 9 and we try to round up, 9 + 1 = 10, so we have to carry over. So 8 (thousands) + 1 (because 9 hundreds + 1 hundred = 10 hundreds = 1 thousand) becomes 9 (thousands), and the hundreds, tens, and ones digits become 0. Wait, I made a mistake earlier. Let's correct that. The number is 8942. The digit in the hundreds place is 9, the digit to the right (tens place) is 4. But wait, no—wait, the rule is: when rounding to the nearest hundred, we look at the tens digit. But if the hundreds digit is 9 and we round up, we have to increase the thousands digit. Let's do it step by step. The number is 8942. We want to round to the nearest hundred. So we look at the tens digit, which is 4. Wait, but 942 is the part after the thousands place? No, 8942 = 8×1000 + 9×100 + 4×10 + 2×1. To round to the nearest hundred, we consider the value of the number modulo 1000 (the thousands part) and the last three digits (942). Wait, no, the standard method is: for a number N, to round to the nearest 100, we find the multiple of 100 closest to N. The multiples of 100 around 8942 are 8900 and 9000. Now, 8942 - 8900 = 42, and 9000 - 8942 = 58. Wait, but that would suggest 8900 is closer, but that's wrong. Wait, no, wait: 8942, the hundreds digit is 9, tens is 4, ones is 2. Wait, no, I think I messed up the digits. Wait, 8 (thousand), 9 (hundred), 4 (ten), 2 (one). So the number is 8 9 4 2. When rounding to the nearest hundred, we look at the digit in the tens place (4) and the digit in the hundreds place (9). Wait, the correct rule is: the digit in the place we are rounding to is the hundreds place (9), and the digit to the right (tens place) is 4. But when the digit in the hundreds place is 9 and we round up, we have to carry over to the thousands place. So 9 + 1 = 10, so the thousands digit (8) becomes 8 + 1 = 9, and the hundreds, tens, and ones digits become 0. So 8942 rounded to the nearest hundred is 9000. Wait, why? Because 8942 is closer to 9000 than to 8900? Wait, 8942 - 8900 = 42, 9000 - 8942 = 58. Wait, that's not closer. Wait, I'm confused. Wait, no, the mistake is in the digit positions. Wait, 8942: let's write it as 8*1000 + 9*100 + 4*10 + 2*1. To round to the nearest hundred, we need to see if the number formed by the tens and ones digits (42) is closer to 0 or 100. Since 42 is less than 50, we should round down? But that would be 8900. But that's not right. Wait, no, the correct way is: when rounding to the nearest hundred, we look at the tens digit. If the tens digit is 5 or more, we round up the hundreds digit; if less than 5, we round down. But when the hundreds digit is 9 and we round up, we have to carry over. So 8942: tens digit is 4 (less than 5), but wait, 942 is the number after the thousands place? No, 8942 is 8 thousand and 942. Wait, 942 rounded to the nearest hundred: the tens digit is 4, so we round 942 to 900, so 8000 + 900 = 8900? But that contradicts the earlier thought. Wait, no, let's use the correct rounding algorithm. The algorithm for rounding to the nearest 100:

1. Find the digit in the hundreds place: in 8942, it's 9 (position: 3rd from the right, since rightmost is position 0: 2 (pos 0), 4 (pos 1), 9 (pos 2), 8 (pos 3)).

2. Look at the digit in the tens place (position 1), which is 4.

3. If the tens digit is less than 5, we keep the hundreds digit as it is and set the tens and ones digits to 0. But if the hundreds digit is 9, and we keep it as 9, then the number would be 8900. But wait, another way: the number 8942 is between 8900 and 9000. The distance from 8942 to 8900 is 42, and to 9000 is 58. So 8900 is closer? But that can't be, because when the tens digit is 4, we round down. But wait, I think I made a mistake in the digit positions. Wait, 8942: digits are:

- Thousands: 8

- Hundreds: 9

- Tens: 4

- Ones: 2

To round to the nearest hundred, we consider the number as a whole. The rule is: the digit in the hundreds place is 9, the digit to the right (tens place) is 4. Since 4 < 5, we round down the hundreds place? But 9 can't be rounded down in the sense of decreasing, because 9 is the highest single - digit number. Wait, no, the correct approach is that when rounding to the nearest hundred, we look at the number formed by the last two digits (tens and ones) which is 42. If the last two digits are less than 50, we round down (keep the hundreds digit the same and set last two to 0); if 50 or more, we round up (add 1 to the hundreds digit and set last two to 0). So 42 < 50, so we round down. So 8942 rounded to the nearest hundred is 8900? But that seems wrong. Wait, no, let's check with a smaller number. Let's take 1942. Rounding 1942 to the nearest hundred: tens digit is 4, so we round to 1900? But 1942 is closer to 1900 than 2000 (1942 - 1900 = 42, 2000 - 1942 = 58). So that's correct. So for 8942, following the same logic, since the last two digits (42) are less than 50, we round down, so 8900? But wait, I think I had a confusion earlier. Wait, no, let's check with the standard rounding rules. The rule for rounding to the nearest 100:

- Look at the tens digit.

- If tens digit ≥5, round up the hundreds digit (add 1 to the hundreds digit, and set tens and ones to 0).

- If tens digit <5, keep the hundreds digit the same, set tens and ones to 0.

In 8942:

- Hundreds digit: 9

- Tens digit: 4 (which is <5)

So we keep the hundreds digit (9) the same, and set tens (4) and ones (2) to 0. So the number becomes 8900. Wait, but earlier I thought about carrying over, but that was a mistake. The carrying over happens when the digit in the place we are rounding to is 9 and we round up. But in this case, we are rounding down, so we don't carry over. So 8942 rounded to the nearest hundred is 8900? Wait, no, wait, 8942: 8 (thousand), 9 (hundred), 4 (ten), 2 (one). So when we round to the nearest hundred, we change the ten and one digits to 0 if we round down. So 9 (hundred) remains, 4 and 2 become 0. So 8900. But now I'm confused because different methods gave different results. Wait, let's use the formula for rounding a number N to the nearest 100:

Let N = 100*a + b, where 0 ≤ b < 100. Then, if b < 50, round to 100*a; if b ≥50, round to 100*(a + 1).

For N = 8942, a = 89 (since 8942 = 100*89 + 42), and b = 42. Since 42 < 50, we round to 100*89 = 8900.

Yes, that's the correct formula. So 8942 rounded to the nearest hundred is 8900. Wait, but I think I made a mistake earlier when I thought about carrying over. The carrying over happens when a + 1 causes a carry, but in this case, a = 89, and we are not adding 1 to a, so no carry over. So the correct answer is 8900? Wait, no, wait, 89*100 is 8900, and 8942 - 8900 = 42, 9000 - 8942 = 58. So 8900 is closer. So the correct rounding is 8900.

Wait, but now I'm really confused because initially I thought it was 9000, but according to the formula, it's 8900. Let's check with an online rounding calculator (mentally). For example, 1234 rounded to the nearest hundred: tens digit is 3 <5, so 1200. 1250 rounded to the nearest hundred: tens digit 5, so 1300. So for 8942, tens digit 4 <5, so 8900. Yes, that makes sense. So my initial mistake was in the digit position understanding. So the correct steps are:

Step1: Determine the relevant digits

For the number 8942, when rounding to the nearest hundred, we focus on the hundreds digit (9) and the digit to its right (the tens digit, which is 4).

Step2: Apply the rounding rule

Since the tens digit (4) is less than 5, we keep the hundreds digit (9) unchanged and set the tens and ones digits to 0. So we replace the 4 (tens) and 2 (ones) with 0s.

Answer:

8900