Decimal places (d.p.) count digits after the decimal point; significant figures (s.f.) count from the first non-zero digit.
Look at the next digit: 5 or more rounds up. 3.4567 to 2 d.p. = 3.46; 0.004567 to 2 s.f. = 0.0046.
Zeros matter: 0.0500 to 3 s.f. keeps the trailing zeros to show precision.
Estimation
Round each number to 1 significant figure and calculate: \frac{39.2 \times 4.8}{0.52}\approx \frac{40 \times 5}{0.5} = 400.
For a quotient with positive inputs, increasing the numerator and decreasing a positive denominator gives an overestimate. If some changes increase and others decrease the result, inspect the effect rather than guessing.
Standard form
Write numbers as A \times 10n where 1 \leq A < 10. 45\,000 = 4.5 \times 104; 0.0032 = 3.2 \times 10-3.
Multiply: multiply the As and add the powers. Divide: divide the As and subtract powers. Adjust A if it leaves the range.
Units and approximations
Always give units. Round at the end, not during a calculation.
Use \approx for approximate equality, and the correct number of significant figures for the data given.
Length, area and volume units
Error intervals
Rounded values give an error interval: 4.6 to 1 d.p. means 4.55 \leq x < 4.65.
Values rounding to 4.6
投影片
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