Find the greatest possible error for the given measurement if it is to the nearest 10 miles.
150 mi
a. 5 mi
b. 75 mi
c. 0.5 mi
d. 7.5 mi
Find the greatest possible error for each measurement.
18.9 m
a. 0.01 m
b. 0.5 m
c. 9.45 m
d. 0.05 m
Find the greatest possible error for each measurement.
4 1/2 oz
a. 1/4 oz
b. 2 1/2 oz
c. 1 oz
d. 2 1/4 oz
Find the greatest possible error for each measurement.
1 3/4 c
a. 1/2 c
b. 1/4 c
c. 1/6 c
d. 1/8 c
Find the greatest possible error for each measurement.
3 ft
a. 1 ft
b. 1/2 ft
c. 1/4 c
d. 1/6 c
Find the greatest possible error for the given measurement if it is to the nearest 10 miles.
350 mi
a. 0.5 mi
b. 5 mi
c. 17.5 mi
d. 175 mi
How do you work the greatest possible error?
It has to do with rounding. If rounding to the nearest 10 miles, and assuming integer values, then
145 - 154 all round to 150
So, the greatest error is 5 miles.
The others work the same way.
1a
150
To find the greatest possible error for a given measurement when it is rounded to a certain interval, you need to consider the halfway point between the actual value and the two values that are on either side of it.
Here's how you can work out the greatest possible error for each question:
1. Given measurement: 150 mi (to the nearest 10 miles)
The halfway point between 150 mi and the next higher value (160 mi) is 155 mi. Similarly, the halfway point between 150 mi and the next lower value (140 mi) is 145 mi.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (155 mi - 145 mi) / 2 = 5 mi.
Hence, the answer is option a. 5 mi.
2. Given measurement: 18.9 m
The halfway point between 18.9 m and the next higher value (19 m) is 18.95 m. Similarly, the halfway point between 18.9 m and the next lower value (18.8 m) is 18.85 m.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (18.95 m - 18.85 m) / 2 = 0.05 m.
Hence, the answer is option d. 0.05 m.
3. Given measurement: 4 1/2 oz
The halfway point between 4 1/2 oz and the next higher value (5 oz) is 4 3/4 oz. Similarly, the halfway point between 4 1/2 oz and the next lower value (4 oz) is 4 1/4 oz.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (4 3/4 oz - 4 1/4 oz) / 2 = 1/4 oz.
Hence, the answer is option a. 1/4 oz.
4. Given measurement: 1 3/4 c
The halfway point between 1 3/4 c and the next higher value (2 c) is 1 7/8 c. Similarly, the halfway point between 1 3/4 c and the next lower value (1 1/2 c) is 1 5/8 c.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (1 7/8 c - 1 5/8 c) / 2 = 1/8 c.
Hence, the answer is option d. 1/8 c.
5. Given measurement: 3 ft (to the nearest whole foot)
The halfway point between 3 ft and the next higher value (4 ft) is 3.5 ft. Similarly, the halfway point between 3 ft and the next lower value (2 ft) is 2.5 ft.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (3.5 ft - 2.5 ft) / 2 = 0.5 ft.
Hence, the answer is option b. 0.5 ft.
6. Given measurement: 350 mi (to the nearest 10 miles)
The halfway point between 350 mi and the next higher value (360 mi) is 355 mi. Similarly, the halfway point between 350 mi and the next lower value (340 mi) is 345 mi.
Therefore, the greatest possible error for this measurement is half the difference between these two values: (355 mi - 345 mi) / 2 = 5 mi.
Hence, the answer is option b. 5 mi.
Remember, when working with greatest possible error, you need to find the halfway point between the actual value and the two values on either side of it, and then calculate half the difference between those two values.