Question

temperature was 37.6°f. estimate the
difference in temperatures.

one way round to the nearest ten.
round 37.6 to the nearest ten.
37.6 →
round 31.3 to the nearest ten.
31.3 →
subtract.

• =

another way round to the nearest one.
round 37.6 to the nearest one.
37.6 →
round 31.3 to the nearest one.
31.3 →
subtract.

• =

the difference is about °f or about °f.
the actual difference is 6.3°f. so, rounding to the nearest
gave the more accurate estimate.

Explanation:

Step1: Analyze the first method (round to nearest ten)

We first round 37.6 to the nearest ten. The digit in the tens place is 3, and the digit in the ones place is 7, which is greater than or equal to 5, so we round up the tens place. So \( 37.6\approx40 \) when rounded to the nearest ten. Then we round 31.3 to the nearest ten. The digit in the tens place is 3, and the digit in the ones place is 1, which is less than 5, so we keep the tens place as it is. So \( 31.3\approx30 \) when rounded to the nearest ten. Then we subtract the two rounded numbers: \( 40 - 30=10 \).

Step2: Analyze the second method (round to nearest one)

We round 37.6 to the nearest one. The digit in the ones place is 7, and the digit in the tenths place is 6, which is greater than or equal to 5, so we round up the ones place. So \( 37.6\approx38 \) when rounded to the nearest one. Then we round 31.3 to the nearest one. The digit in the ones place is 1, and the digit in the tenths place is 3, which is less than 5, so we keep the ones place as it is. So \( 31.3\approx31 \) when rounded to the nearest one. Then we subtract the two rounded numbers: \( 38 - 31 = 7 \).

Step3: Determine the more accurate estimate

The actual difference is \( 37.6-31.3 = 6.3^{\circ}\text{F} \). We compare the two estimated differences (10 and 7) with the actual difference (6.3). The difference between 7 and 6.3 is \( |7 - 6.3|=0.7 \), and the difference between 10 and 6.3 is \( |10 - 6.3| = 3.7 \). Since \( 0.7<3.7 \), rounding to the nearest one gives a more accurate estimate.

Answer:

The difference is about \( \boldsymbol{10} \) \(^{\circ}\text{F}\) or about \( \boldsymbol{7} \) \(^{\circ}\text{F}\). The actual difference is \( 6.3^{\circ}\text{F} \). So, rounding to the nearest \( \boldsymbol{\text{one}} \) gave the more accurate estimate.