Question

1. estimate the difference. round each number to the nearest whole number, then subtract.

\\( 15 \frac{89}{100} - 13 \frac{19}{49} \\)

1. the difference is approximately \\( \square \\).

Explanation:

Step1: Round the first mixed number

The first number is \(15\frac{89}{100}\). The fraction \(\frac{89}{100}=0.89\), which is close to 1, but wait, no—wait, to round to the nearest whole number, we look at the fractional part. \(\frac{89}{100}=0.89\), which is less than 1, but wait, \(15\frac{89}{100}\) is 15.89, so rounding to the nearest whole number: since 0.89 ≥ 0.5, we round up? Wait, no: 15.89, the nearest whole number is 16? Wait, no, 15.89 is between 15 and 16. The decimal part is 0.89, which is more than 0.5, so we round 15.89 to 16? Wait, no, wait: 15 + 0.89 = 15.89. Rounding to the nearest whole number: if the decimal part is ≥ 0.5, we round up. So 15.89 rounds to 16? Wait, no, wait, 15.89 is 15 + 0.89. So the nearest whole number is 16? Wait, no, 15.89 is closer to 16? Wait, 15.89 - 15 = 0.89, 16 - 15.89 = 0.11. Wait, no, that's not right. Wait, 15.89 is 15 and 89 hundredths. So the distance to 15 is 0.89, to 16 is 0.11? No, that's reversed. Wait, 16 - 15.89 = 0.11, and 15.89 - 15 = 0.89. So actually, 15.89 is closer to 16? Wait, no, 0.89 is more than 0.5, so we round up. So 15.89 rounds to 16? Wait, no, wait, 15.89: the whole number part is 15, the decimal is 0.89. So when rounding to the nearest whole number, we look at the tenths place? Wait, no, the rule is: look at the first decimal place (tenths) to round to the nearest whole number? Wait, no, the standard rule is: to round a number to the nearest whole number, look at the digit in the tenths place (the first decimal place). If it's 5 or more, round up; if less, round down. Wait, 15.89: the tenths digit is 8, which is more than 5, so we round up the whole number part. So 15 becomes 16. So \(15\frac{89}{100}\) rounds to 16.

Step2: Round the second mixed number

The second number is \(13\frac{19}{49}\). Let's convert the fraction to a decimal: \(\frac{19}{49} \approx 0.3878\). So the mixed number is \(13 + 0.3878 = 13.3878\). Now, round this to the nearest whole number. The decimal part is 0.3878, which is less than 0.5, so we round down. So \(13\frac{19}{49}\) rounds to 13.

Step3: Subtract the rounded numbers

Now, subtract the rounded numbers: 16 - 13 = 3.

Wait, but let's check again. Wait, maybe I made a mistake in rounding the first number. Wait, \(15\frac{89}{100}\) is 15.89, which is 15 + 0.89. So rounding to the nearest whole number: 15.89 is closer to 16? Wait, 15.89 is 15.89, so the nearest whole number is 16. Then the second number: \(13\frac{19}{49}\) is approximately 13.39, which rounds to 13. Then 16 - 13 = 3. But wait, maybe I messed up the first rounding. Wait, \(15\frac{89}{100}\): the fraction is 89/100, which is 0.89, so the mixed number is 15.89. Rounding to the nearest whole number: 15.89 is 15 + 0.89. The rule is: if the decimal part is ≥ 0.5, round up. 0.89 ≥ 0.5, so round up to 16. The second number: 13.3878, decimal part 0.3878 < 0.5, so round down to 13. Then 16 - 13 = 3. So the estimated difference is 3.

Answer:

3