Question

Determine the following estimate without using a calculator. Then use a calculator to perform the computation necessary to obtain an exact answer. How reasonable is your estimate when compared to the actual answer? Estimate the total cost of six grocery items if their prices are $4.21, $7.19, $12.68, $2.02, $10.24, and $6.63, by rounding each price to the nearest dollar and then adding.

Answer 1

Answer:

Estimate: $43

Exact: $42.97

Explanation:

1. First we must identify the rules of rounding.

    Any number you want to round to (ie: the nearest dollar, tenth, ect) you must look at the number behind it (ie: looking at the ones spot when asked to round to the nearest ten). This number behind is called the rounding digit.

    If the rounding digit we are asked to round is a 0, 1, 2, 3, or 4, then we make the rounding digit and every number behind it a 0. This is call rounding down.

    If the rounding digit we are asked to round to is a 5, 6, 7 , 8, or 9, then we make the rounding digit and every number behind it a 0. The number in front of the rounding digit (the place value we were asked to round to) becomes 1 digit higher. This is called rounding down.

2. We will now round all the numbers to the nearest dollar. So, our rounding digit will be the number behind the dollars, the tenths place.

    4.21 → 4.21 → rounding down → 4.00 → 4

    7.19 → 7.19 → rounding down → 7.00 → 7

    12.68 → 12.68 → rounding up → 13.00 → 13

    2.02 → 2.02 → rounding down → 2.00 → 2

    10.24 → 10.24 → rounding down → 10.00 → 10

    6.63 → 6.63 → rounding up → 7.00 → 7

3. Next, we will take all our rounded numbers and add them up.

    4 + 7 = 11

           ↓

  11 + 13 = 24

           ↓

  24 + 2 = 26

           ↓

 26 + 10 = 36

           ↓

   36 + 7 = 43

4. Then, add up all the original prices.

      4.21 + 7.19 = 11.40

                     ↓

   11.40 + 12.68 = 24.08

                     ↓

    24.08 + 2.02 = 26.10

                     ↓

    26.10 + 10.24 = 36.34

                     ↓

     36.34 + 6.63 = 42.97

5. The estimate, when compared to the actual answer, is very comparable because the estimate is only $0.03 more than the actual amount. The two are less than 10¢ away from each other. The efficiency had when rounding and the close proximity to the real answer makes the two very comparable.