Error Intervals Flashcards

All 5 cards in this deck

What are the steps to write an error interval for a rounded value?
e.g. $x$ rounded to 1 decimal place is $9.8$

1. Halve the rounding unit: $0.1 \div 2 = 0.05$
2. Subtract and add it: $9.75$ and $9.85$
3. Write the interval: $9.75 \le x < 9.85$

In an error interval for a rounded value, why is the upper limit written with $<$ rather than $\le$?

Because a value equal to the upper limit would round up to the next value instead.
e.g. $9.85$ rounds to $9.9$, not $9.8$

What does it mean to truncate a number to 1 decimal place?

Cut off (throw away) all digits after the first decimal place, without rounding.
e.g. $8.37$ truncated to 1 dp is $8.3$

How do you write the error interval for a truncated value?
e.g. $y$ truncated to 1 decimal place gives $8.3$

The truncated value is the lower limit and the next value at that accuracy is the upper limit: $8.3 \le y < 8.4$

True or false? If $x = 4700$ correct to 2 significant figures, the error interval is $4699.5 \le x < 4700.5$

False. To 2 sf the rounding unit is $100$, so the interval is $4650 \le x < 4750$