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Maths skills: decimals, standard form, estimation and significant figures
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Psychology papers include calculations. These number skills help you handle data accurately, especially very large or very small numbers.
Decimals and standard form
Standard form writes a number as A × 10n, where A is at least 1 and less than 10.
Large numbers: 45 000 = 4.5 × 104 (the decimal point moves 4 places).
Small numbers: 0.0032 = 3.2 × 10-3 (the point moves 3 places the other way, so the power is negative).
To turn standard form back into a decimal, move the point the number of places shown by the power.
Large numbers: 45 000 = 4.5 × 104 (the decimal point moves 4 places).
Small numbers: 0.0032 = 3.2 × 10-3 (the point moves 3 places the other way, so the power is negative).
To turn standard form back into a decimal, move the point the number of places shown by the power.
Significant figures
Significant figures (s.f.) count from the first non-zero digit.
To round to 2 s.f., look at the third digit: 5 or more rounds up.
Examples: 2347 to 2 s.f. = 2300. 0.04782 to 2 s.f. = 0.048. 68.25 to 3 s.f. = 68.3.
In psychology, means and percentages are often given to 1 or 2 decimal places or 2 or 3 s.f. Do not give more figures than the data justifies.
To round to 2 s.f., look at the third digit: 5 or more rounds up.
Examples: 2347 to 2 s.f. = 2300. 0.04782 to 2 s.f. = 0.048. 68.25 to 3 s.f. = 68.3.
In psychology, means and percentages are often given to 1 or 2 decimal places or 2 or 3 s.f. Do not give more figures than the data justifies.
Estimation
Estimating means rounding numbers to make a quick, rough calculation, to check whether an answer is sensible.
Round each number to 1 significant figure first.
Example: 48 participants each recall about 19 words. Estimate: 50 × 20 = 1000 words in total (the exact answer is 912).
If your calculator gives 9120, the estimate shows you have made a mistake.
Round each number to 1 significant figure first.
Example: 48 participants each recall about 19 words. Estimate: 50 × 20 = 1000 words in total (the exact answer is 912).
If your calculator gives 9120, the estimate shows you have made a mistake.
A study records a reaction time of 0.00052 seconds. Write this in standard form.
- The first non-zero digit is 5, so A = 5.2.
- The decimal point moves 4 places to the right to get 5.2, so the power is -4.
Answer: 5.2 × 10-4 seconds.
Standard form is A × 10n with A between 1 and 10; small numbers have negative powers. Significant figures count from the first non-zero digit. Estimation rounds to 1 s.f. to check answers.
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