Question

using reasoning and estimation to calculate with decimals - item 992311
the image shows a set of beginning steps you can use to divide 59.50 by 6.8.
complete the sentences below that describe where to put the decimal point in
the answer.

round each number to the nearest whole.
59.50 is closest to and 6.8 is closest to .

for an answer close to the quotient of the estimates, place the decimal between .

Explanation:

Step1: Round 59.50 to nearest whole

A number with a decimal part of 0.5 or higher rounds up. 59.50 has 0.50, so it rounds to 60.

Step2: Round 6.8 to nearest whole

6.8 has a decimal part 0.8 which is ≥0.5, so it rounds up to 7.

Step3: Estimate the quotient

Divide the rounded numbers: \( \frac{60}{7} \approx 8.57 \). The long - division result is 0875 (which is 8.75). Comparing to the estimate, the decimal should be between 8 and 7 (i.e., after the 8, making it 8.75, so between 8 and 7? Wait, no, the number is 0875, so placing the decimal between 8 and 7? Wait, the quotient from long division is 8.75. The estimate \( 60\div7\approx8.57 \), so the decimal should be between 8 and 7? Wait, no, the number is 0875, so to get 8.75, we place the decimal between 8 and 7 (so 8.75). So the decimal is between 8 and 7 (or more precisely, after the first digit 8, so between 8 and 7 in the number 0875, making it 8.75).

Answer:

59.50 is closest to 60 and 6.8 is closest to 7. For an answer close to the quotient of the estimates, place the decimal between 8 and 7 (to get 8.75, matching the estimate - related placement).