Question

rounding numbers (level 2)
question
round 69.08509571 to the nearest hundred - thousandth.
answer
attempt 1 out of 2

Explanation:

Step1: Identify the place value

The hundred - thousandth place is the 5th digit after the decimal point. For the number \(69.08509571\), let's list the digits after the decimal:
- 1st digit (tenths): \(0\)
- 2nd digit (hundredths): \(8\)
- 3rd digit (thousandths): \(5\)
- 4th digit (ten - thousandths): \(0\)
- 5th digit (hundred - thousandths): \(9\)
- 6th digit (millionths): \(5\)

Step2: Check the next digit for rounding

To round to the nearest hundred - thousandth, we look at the digit in the millionths place (the digit to the right of the hundred - thousandth place). The digit in the millionths place is \(5\). When the digit to the right is \(5\) or greater, we round up the digit in the hundred - thousandth place.

The digit in the hundred - thousandth place is \(9\). Rounding up \(9\) gives \(10\), so we carry over the \(1\) to the ten - thousandths place. The ten - thousandths place digit is \(0\), adding the carried over \(1\) gives \(1\), and the hundred - thousandths place becomes \(0\).

Now, let's rewrite the number:
The number before the decimal is \(69\). After the decimal, the tenths place is \(0\), hundredths is \(8\), thousandths is \(5\), ten - thousandths is \(1\), and hundred - thousandths is \(0\) (after rounding). So the number rounded to the nearest hundred - thousandth is \(69.08510\) (we can also write it as \(69.08510\) or \(69.0851\) but since we are rounding to the hundred - thousandth place, we need to show the digit in that place. Wait, let's re - examine:

Wait, the number is \(69.08509571\). Let's index the decimal digits:

Decimal digits: position 1: \(0\) (tenths), position 2: \(8\) (hundredths), position 3: \(5\) (thousandths), position 4: \(0\) (ten - thousandths), position 5: \(9\) (hundred - thousandths), position 6: \(5\) (millionths), position 7: \(7\) (ten - millionths), position 8: \(1\) (hundred - millionths)

To round to the hundred - thousandth place (position 5), we look at position 6 (millionths place) which is \(5\). So we round up position 5. Position 5 is \(9\), so \(9 + 1=10\). We carry over the \(1\) to position 4 (ten - thousandths place). Position 4 is \(0\), so \(0+1 = 1\), and position 5 becomes \(0\).

So the number rounded to the nearest hundred - thousandth is \(69.08510\) (or \(69.0851\) if we consider that trailing zeros after the last non - zero digit in the decimal may be omitted, but for the hundred - thousandth place, the digit in the hundred - thousandth place is the 5th digit after the decimal, so we need to have that digit. Wait, actually, the correct way is:

\(69.08509571\)

Hundred - thousandth place: 5th digit after decimal: \(9\)

Next digit (6th): \(5\)

So round up the 5th digit: \(9+1 = 10\), so we add 1 to the 4th digit (ten - thousandths place: \(0\)): \(0 + 1=1\), and set the 5th digit to \(0\).

So the number is \(69.08510\) (we can write it as \(69.08510\) or \(69.0851\) but since the hundred - thousandth place is the 5th digit, and after rounding, the number is \(69.08510\) (the trailing zero in the hundred - thousandth place is significant for the place value).

Wait, let's do it step by step:

Original number: \(69.08509571\)

Digits after decimal: \(0\) (1), \(8\) (2), \(5\) (3), \(0\) (4), \(9\) (5), \(5\) (6), \(7\) (7), \(1\) (8)

We want to round to the 5th digit (hundred - thousandth). The 6th digit is \(5\), which is \(\geq5\), so we round up the 5th digit.

5th digit is \(9\), so \(9+1 = 10\). So we carry over 1 to the 4th digit.

4th digit is \(0\), \(0 + 1=1\). Now the 5th digit becomes \(0\).

So the number becomes \(69.08510\) (because the 4th digit is now \(1\), 5th is \(0\)).

Answer:

\(69.08510\) (or \(69.0851\) but more accurately \(69.08510\) when considering the hundred - thousandth place)