Question

question
round 1.988 to the nearest tenth.

answer attempt 1 out of 2

Explanation:

Step1: Identify the tenths and hundredths place

The number is \(1.988\). The tenths place is \(9\) and the hundredths place is \(8\).

Step2: Apply rounding rule

When rounding to the nearest tenth, we look at the hundredths place. If the digit in the hundredths place is \(5\) or greater, we round up the tenths place. Here, the hundredths digit is \(8\) (which is \( \geq 5\)), so we add \(1\) to the tenths place.

The tenths place digit is \(9\), adding \(1\) to \(9\) gives \(10\). So we carry over the \(1\) to the ones place. The ones place was \(1\), adding the carried over \(1\) gives \(2\), and the tenths place becomes \(0\) (after carrying over). But wait, actually, let's do it step by step. \(1.988\) rounded to the nearest tenth:

\(1.988\) - tenths digit \(9\), hundredths digit \(8\). Since \(8 \geq 5\), we increase the tenths digit by \(1\). \(9 + 1 = 10\), so we write \(0\) in the tenths place and carry over \(1\) to the ones place. The ones place was \(1\), so \(1 + 1 = 2\). So the number rounded to the nearest tenth is \(2.0\). Wait, no, wait. Wait, \(1.988\): the tenths place is \(9\), hundredths is \(8\). So rounding \(1.988\) to the nearest tenth:

The rule is: look at the digit to the right of the tenths place (hundredths place). If it's \( \geq 5\), round up the tenths place.

So \(1.988\): tenths digit is \(9\), hundredths is \(8\) (which is \( \geq 5\)). So we add \(1\) to the tenths digit: \(9 + 1 = 10\). So we have to carry over. So the tenths place becomes \(0\), and we add \(1\) to the ones place. The ones place was \(1\), so \(1 + 1 = 2\). So the number becomes \(2.0\)? Wait, no, that's not right. Wait, no, let's think again. Wait, \(1.988\) is closer to \(2.0\) when rounded to the nearest tenth? Wait, no, \(1.988\) is \(1.9\) plus \(0.088\). The tenth is \(0.1\) increments. So \(1.9\) is \(1.9\), \(2.0\) is the next tenth. The distance from \(1.988\) to \(1.9\) is \(0.088\), and to \(2.0\) is \(0.012\). Wait, no, that's not right. Wait, \(1.988 - 1.9 = 0.088\), \(2.0 - 1.988 = 0.012\). So yes, it's closer to \(2.0\). But wait, when rounding \(1.988\) to the nearest tenth, the correct way is:

\(1.988\)

Tenths place: \(9\)

Hundredths place: \(8\) (which is \( \geq 5\)), so round up the tenths place.

\(9 + 1 = 10\), so we carry over. So the tenths digit becomes \(0\), and we add \(1\) to the ones digit. The ones digit was \(1\), so \(1 + 1 = 2\). So the number is \(2.0\)? Wait, but \(2.0\) to the nearest tenth is \(2.0\), but is that correct? Wait, no, wait, maybe I made a mistake. Wait, \(1.988\) rounded to the nearest tenth:

Wait, the tenths place is the first digit after the decimal. So \(1.988\) is \(1\) (ones), \(9\) (tenths), \(8\) (hundredths), \(8\) (thousandths).

To round to the nearest tenth, we look at the hundredths digit (the digit to the right of the tenths place). The hundredths digit is \(8\), which is greater than or equal to \(5\), so we round up the tenths digit.

The tenths digit is \(9\), so adding \(1\) to \(9\) gives \(10\). So we have to carry over. So the tenths place becomes \(0\), and we add \(1\) to the ones place. The ones place was \(1\), so \(1 + 1 = 2\). So the number rounded to the nearest tenth is \(2.0\). Wait, but \(2.0\) is the same as \(2\), but when rounding to the nearest tenth, we should have one decimal place. So \(2.0\) is correct because we need to show the tenths place. Alternatively, is it \(2.0\) or \(2\)? Wait, no, when rounding to the nearest tenth, we need to have a digit in the tenths place. So \(1.988\) rounded to the nearest tenth is \(2.0\). Wait, but let's check with a calculator. If you round \(1.988\) to the nearest tenth, what do you get? Let's see: \(1.988\) - the tenths place is \(9\), hundredths is \(8\). So round up: \(1.9 + 0.1 = 2.0\). Yes, because \(1.988\) is closer to \(2.0\) than to \(1.9\). Because the difference between \(1.988\) and \(1.9\) is \(0.088\), and between \(1.988\) and \(2.0\) is \(0.012\). So \(0.012 < 0.088\), so it's closer to \(2.0\). So the correct rounded value is \(2.0\). Wait, but sometimes people write \(2.0\) to show the tenth place, or just \(2\). But in decimal form, to the nearest tenth, it's \(2.0\). Wait, no, wait, \(1.988\) rounded to the nearest tenth:

Wait, maybe I messed up. Let's do it again. The tenths place is the first decimal digit. So \(1.988\):

- Tenths place: \(9\)
- Hundredths place: \(8\) (digit to the right of tenths place)

Since \(8 \geq 5\), we round up the tenths place. So \(9 + 1 = 10\), so we carry over. So the tenths place becomes \(0\), and we add \(1\) to the ones place. The ones place was \(1\), so \(1 + 1 = 2\). So the number is \(2.0\) (because we need to have one decimal place when rounding to the nearest tenth). So the answer is \(2.0\) or \(2\)? Wait, no, \(2.0\) is more accurate because it shows that we rounded to the tenth place. For example, if you round \(1.95\) to the nearest tenth, it's \(2.0\), not \(2\), because the tenth place is significant. So in this case, \(1.988\) rounded to the nearest tenth is \(2.0\). Wait, but let's check with another approach. Let's consider the number line. The tenths are \(1.9, 2.0, 2.1, \dots\). The number \(1.988\) is between \(1.9\) and \(2.0\). The midpoint between \(1.9\) and \(2.0\) is \(1.95\). Since \(1.988 > 1.95\), it's closer to \(2.0\) than to \(1.9\). So we round up to \(2.0\). So the correct answer is \(2.0\), but sometimes it's written as \(2\), but in decimal form with one decimal place, it's \(2.0\). Wait, but the problem says "round to the nearest tenth", so we need to have a digit in the tenths place. So \(2.0\) is correct. Wait, but maybe I made a mistake earlier. Let's do it step by step again:

Number: \(1.988\)

1. Identify the place to round to: tenths place (the first decimal digit, which is \(9\)).

2. Look at the digit to the right of the tenths place: hundredths place, which is \(8\).

3. Since \(8 \geq 5\), we round up the tenths place digit.

4. The tenths place digit is \(9\), so \(9 + 1 = 10\). We can't have \(10\) in the tenths place, so we carry over \(1\) to the ones place.

5. The ones place digit is \(1\), so \(1 + 1 = 2\), and the tenths place becomes \(0\) (after carrying over).

6. So the number rounded to the nearest tenth is \(2.0\) (because we need to show the tenths place, even if it's \(0\)).

Yes, that makes sense. So the answer is \(2.0\), but sometimes it's acceptable to write \(2\), but in the context of rounding to the nearest tenth, \(2.0\) is more precise as it indicates the tenths place.

Answer:

\(2.0\)