Error intervals
The Maths Habit
A report says about 40 people came to a party.
How many people could have come?
Any number from 35 to 44, if 40 is to the nearest 10
- Error interval
- The range of values a number could have been before it was rounded.
- Lower bound
- The smallest value it could have been.
- Upper bound
- The value it must have been below.
x = 40, correct to the nearest 10
304050
≤ x <
x rounds to 40, to the nearest 10.
Could x have been 45?
No. 45 rounds up to 50.
What is halfway between 80 and 90?
85
The error interval for h is 165 ≤ h < 175.
What was h rounded to, and to what accuracy?
170 (halfway), to the nearest 10
Which symbol goes with the upper bound?
< or ≤
<
a = 500, to the nearest 100
400500600
450 ≤ a < 550
half of 100 is 50
500 − 50 and 500 + 50
b = 900, to the nearest 100
8009001000
850 ≤ b < 950
a = 500, to the nearest 100
400500600
450 ≤ a < 550
d = 6000, to the nearest 1000
500060007000
5500 ≤ d < 6500
a = 500, to the nearest 100
400500600
450 ≤ a < 550
g = 80, to the nearest 10
708090
75 ≤ g < 85
a = 500, to the nearest 100
400500600
450 ≤ a < 550
h = 3000, to the nearest 100
290030003100
2950 ≤ h < 3050
a = 500, to the nearest 100
400500600
450 ≤ a < 550
k = 450, to the nearest 10
440450460
445 ≤ k < 455
y = 3.2, correct to 1 decimal place
3.13.23.3
≤ y <
m = 15, correct to the nearest whole number
141516
≤ m <
A number is truncated to 1 decimal place. The result is 3.7. Write the error interval for the number, x.
3.7 ≤ x < 3.8y = 2500, correct to 2 significant figures. Write the error interval for y.
2450 ≤ y < 2550
t = 300, correct to the nearest 100. Write the error interval for t.
250 ≤ t < 350k = 4.7, correct to 1 decimal place. Write the error interval for k.
4.65 ≤ k < 4.75The error interval for w is 1.25 ≤ w < 1.35. What was w rounded to, and to what accuracy?
1.3, to 1 decimal place
Exit tickets to print
