Question

1. hundredths 49.995

Explanation:

Step1: Identify the hundredths place

In the decimal number \(49.995\), the digits after the decimal point are in the tenths, hundredths, and thousandths places. The second digit after the decimal is the hundredths place, which is \(9\) (the first \(9\) after the decimal is tenths, the second is hundredths, and the third is thousandths). But we need to round to the hundredths place? Wait, the problem says "Hundredths" – maybe we need to look at the value in the hundredths place or round to the hundredths place? Wait, the number is \(49.995\). Let's clarify: the hundredths place is the second digit after the decimal. So in \(49.995\), the digits are:
- Whole number part: \(49\)
- Decimal part: \(9\) (tenths), \(9\) (hundredths), \(5\) (thousandths)

If we are to round \(49.995\) to the hundredths place, we look at the thousandths place (which is \(5\)). When rounding, if the digit to the right (thousandths place here) is \(5\) or more, we round up the hundredths place.

Step2: Round the hundredths place

The hundredths place is \(9\), and the thousandths place is \(5\). So we add \(1\) to the hundredths place: \(9 + 1 = 10\). Since we can't have \(10\) in a single digit, we carry over to the tenths place. The tenths place is also \(9\), so \(9 + 1 = 10\) again, carrying over to the ones place of the whole number. Wait, let's do it step by step:

Starting from the thousandths place: \(5\) ≥ \(5\), so we round up the hundredths place.

Hundredths digit: \(9\) becomes \(9 + 1 = 10\). So we write \(0\) in the hundredths place and carry over \(1\) to the tenths place.

Tenths digit: \(9 + 1 = 10\). Write \(0\) in the tenths place and carry over \(1\) to the ones place of the decimal part's left (the whole number's decimal part? Wait, the whole number is \(49\), so the decimal part is after the decimal. Wait, maybe I misinterpreted. Wait, the number is \(49.995\). Let's represent it as:

\(49.995 = 49 + 0.9 + 0.09 + 0.005\)

To round to the hundredths place, we look at the thousandths digit (\(5\)) to decide. Since \(5 \geq 5\), we round up the hundredths place.

Hundredths place: \(0.09 + 0.01 = 0.10\) (because we add \(0.01\) to the hundredths place). Then, \(0.9 + 0.10 = 1.0\) (tenths and hundredths combined). Then, \(49 + 1.0 = 50.00\)? Wait, no, let's do decimal rounding properly.

Wait, maybe the problem is just to identify the value in the hundredths place or round to the hundredths place. Wait, the original number is \(49.995\). If we are to find the value rounded to the hundredths place, it's \(50.00\)? Wait, no, let's check again.

Wait, maybe the question is to round \(49.995\) to the nearest hundredth. Let's do that:

1. Locate the hundredth place: the second digit after the decimal, which is \(9\) (the digit \(9\) in \(49.9\boldsymbol{9}5\)).
2. Look at the digit to the right (thousandth place): \(5\).
3. Since \(5 \geq 5\), we round up the hundredth place.
4. Rounding up \(9\) in the hundredth place: \(9 + 1 = 10\), so we carry over \(1\) to the tenth place.
5. The tenth place is also \(9\), so \(9 + 1 = 10\), carry over \(1\) to the ones place of the whole number.
6. The ones place of the whole number is \(9\) (wait, the whole number is \(49\), so the ones place is \(9\) (from \(4\boldsymbol{9}\))? Wait, no: \(49\) is \(4\) tens and \(9\) ones. So adding \(1\) to the ones place: \(9 + 1 = 10\), so we carry over \(1\) to the tens place.
7. Tens place: \(4 + 1 = 5\).

So putting it all together, rounding \(49.995\) to the nearest hundredth gives \(50.00\). But maybe the question is just to identify the hundredth digit? Wait, the original number's hundredth digit is \(9\), but if we round, it becomes \(0\) with carryover. Wait, the problem says "Hundredths" – maybe it's about the place value or rounding. Let's assume we need to round \(49.995\) to the hundredths place.

Answer:

If we round \(49.995\) to the nearest hundredth, the result is \(50.00\). If we are just identifying the hundredths place value before rounding, it's \(9\), but with rounding, it becomes \(0\) (after carryover). Wait, maybe the problem is to round to the hundredths place. So the answer is \(50.00\).