Estimate the total weight of two boxes that weigh 9.4 lb and 62.6 lb using rounding and compatible numbers. Which estimate is closer to the actual weight?Why?
To estimate the total weight of two boxes, we can use rounding and compatible numbers.
First, let's round the weights of the boxes to the nearest whole number:
- The weight of the first box, 9.4 lb, can be rounded to 9 lb.
- The weight of the second box, 62.6 lb, can be rounded to 63 lb.
Next, let's find compatible numbers that we can use for estimation. Compatible numbers are numbers that are easy to work with mentally and make calculations simpler. In this case, we can use 10 as a compatible number since it is close to both 9 and 63.
By using compatible numbers, we can multiply the rounded weights by 10 and then add them:
- 9 lb can be rounded to 10 lb.
- 63 lb can be rounded to 60 lb.
Therefore, the total weight can be estimated as 10 lb + 60 lb = 70 lb.
To determine which estimate (rounding or compatible numbers) is closer to the actual weight, we need to compare it to the exact sum of the weights.
The actual sum of the weights is 9.4 lb + 62.6 lb = 72 lb.
Comparing the estimates:
- Rounding: 70 lb
- Compatible numbers: 72 lb
In this case, the estimate using compatible numbers (72 lb) is closer to the actual weight (72 lb) than the estimate using rounding (70 lb). Therefore, the estimate using compatible numbers is more accurate in this situation.