Flashcards · 6 cards

Approximation & error

Say the answer to yourself, then check. Cards you know come back less and less often; cards you don't come back tomorrow.

Rule
Round 3.4671 to 2 decimal places.
Answer
Look at the next digit: 7 is 5 or more, so round up to $3.47$ .
Which neighbour is nearer?Past the halfway mark, round up
From the lesson: Approximation and error
Know it
What is the first significant figure of $0.007596$ ? Round it to 3 significant figures.
Answer
7: zeros at the front don't count. To 3 s.f. it is $0.00760$ , and that last 0 stays because it is significant.
From the lesson: Approximation and error
Know it
In a long calculation, when do you round?
Answer
At the end. Rounding part-way makes the final answer drift.
From the lesson: Approximation and error
Rule
The formula for percentage error?
Answer
$\dfrac{\text{error}}{\text{actual value}} \times 100\%$ . Divide by the actual value, not the measured one.
Percentage errorCompare the error with the actual value
From the lesson: Approximation and error
Know it
A length is measured as 1.65 m but is really 1.60 m. What is the percentage error?
Answer
The error is $1.65 - 1.60 = 0.05$ m, so $\dfrac{0.05}{1.60} \times 100\% = 3.125\%$ .
From the lesson: Approximation and error
Which method?
WAEC 2019 · Paper 1 · Q4
Simplify, correct to three significant figures, $(27.63)^2 - (12.37)^2$ .
What makes this quick?
Answer
It is a difference of two squares: $a^2 - b^2 = (a - b)(a + b)$ , and $27.63 + 12.37$ is a round number.
From the lesson: Approximation and error Try the question