Mathematical Content & Computation (OCR GCSE Psychology): Revision Note

Decimals & standard form

• Psychologists use basic maths to collect, analyse, and present data clearly

• This includes working with:

  • decimals

  • fractions

  • ratios

  • percentages

  • standard form

  • significant figures

• These skills ensure that numerical results are accurate, consistent, and easy to interpret

Decimals

• Decimals include a decimal point to separate whole numbers from parts of a whole

• For example:

  • 6.31 = 6 units and 31 hundredths

  • 20.059 = 20 whole units and 59 thousandths

• Decimals are useful when showing results such as reaction times (e.g. 1.53 seconds) or correlation coefficients (e.g. r = 0.87)

• If numbers are rounded, researchers should always report to a consistent number of decimal places to avoid losing accuracy

Standard form

• Standard form expresses very large or very small numbers in a shorter way

• For example:

  • 835,000,000,000 = 8.35 × 10¹¹

  • 0.000000000000761 = 7.61 × 10⁻¹³

• This is useful when reporting brain measurements, cell counts, or tiny time intervals in psychological research

Fractions & ratios

Fractions

• Fractions show parts of a whole

• For example:

  • 5 out of 25 participants scored above 100 = 5/25

  • 16 out of 100 participants preferred blue = 16/100

• Fractions should be simplified using the highest common factor, e.g.
  5/25 = 1/5  16/100 = 4/25

• To convert a fraction into a decimal, divide the numerator by the denominator

• For example:

  • 1 ÷ 5 = 0.2

  • 4 ÷ 25 = 0.16

Ratios

• Ratios compare quantities or proportions in a data set

• For example:

  • 5 out of 25 participants scored above 100 = 5:25

    • This can be simplified to 1:5

  • A group with a mean of 15 and another with a mean of 5 gives a ratio of 15:5

    • This can be simplified to 3:1

• Ratios are beneficial for comparing groups or conditions, e.g. males vs. females, or experimental vs. control conditions

Percentages

• Percentages show a proportion out of 100 and are often used when comparing different groups or conditions

• For example:

  • 63 out of 70 participants chose option A

    • (63 ÷ 70) × 100 = 90%

  • 15 out of 82 scored below average

    • (15 ÷ 82) × 100 = 18.3%

• Percentages make it easier to compare samples of different sizes, such as test pass rates or questionnaire responses

• Percentages can be expressed as a fraction or a decimal, e.g.

  • 65% as a decimal is 0.65

    • As a fraction, it is 13/20

  • 3% as a decimal is 0.03

    • As a fraction, it is 3/100

Significant figures & estimating results

Significant figures

• Significant figures show how precisely a number is reported

  • They start from the first non-zero digit, not necessarily after the decimal point

• For example:

  • 0.00038967 = 0.00039 (2 significant figures)

  • 65.0 = 3 significant figures

  • 7.0016 = 5 significant figures

• Significant figures help present data accurately but concisely, especially in statistics or when rounding results for clarity

Estimating results

• When working with large numbers, researchers can estimate by rounding up or down

• For example:

  • 619 × 280 can be estimated as 600 × 300 = 180,000

• Estimation allows quick, approximate calculations and helps check that final results are realistic