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Mathematical Requirements for Research Methods

Decimal and standard form, percentages and ratios

  • 3 things to know
  • Component 01

Overview

Recall questions on comparing and converting values in standard form and decimal form, the direction of decimal point shifts, calculating percentages, and expressing a gender split as a ratio in its simplest form.

What you need to know

Answer each one before you reveal it.

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Numbers

In an observation, 45 of the 120 recorded behaviours were aggressive. What percentage is this?

Numbers

Which is the larger value, 3.0 × 10⁻³ or 5.0 × 10⁻⁴, and how many times larger is it?

Key term

Convert 3.2 × 10⁻² into decimal form.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Which is the larger value, 3.0 × 10⁻³ or 5.0 × 10⁻⁴, and how many times larger is it?

    Model answer

    3.0 × 10⁻³ is the larger value and it is six times the size of 5.0 × 10⁻⁴.

  2. 2

    Write 0.0045 in standard form.

    Model answer

    It is written as 4.5 × 10⁻³.

  3. 3

    Convert 3.2 × 10⁻² into decimal form.

    Model answer

    In decimal form it is 0.032.

  4. 4

    A results table records a value as 1.25 × 10⁴. State this in decimal form.

    Model answer

    It is 12,500.

  5. 5

    Why might a researcher convert values from standard form into decimal form before drawing a pie chart?

    Model answer

    Because the sector sizes have to be worked out from ordinary decimal amounts, which are easier to compare and to convert into degrees.

  6. 6

    What tells you the direction of the decimal point shift in standard form?

    Model answer

    A positive power of ten means the number is larger than 10 and the point moves right, while a negative power means it is smaller than 1 and the point moves left.

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