# Recognise expressions in decimal and standard forms

Many of the numbers that occur in science data sets and calculations are complex either by being very large (e.g. sizes of the scale of the universe) or very small (e.g. size of cell or electron). Similarly, most of the data collected in experiments by students may well involve multiple decimal places. As such, students need to be familiar and confident with working with both decimal and standard form as well as performing calculations with them without errors.

Decimals can also be described as fractions where the denominator is a power of 10. We write decimal fractions with a decimal point.

Based on the fact that 1/10 is 0.1 pupils may wrongly generalise that for example 1/6 is 0.6.

When converting between ordinary and standard form some pupils may incorrectly connect the power to the number of zeros; e.g. 4 × 105 = 400 000 so 4.2 × 105 = 4 200 000

Similarly, when working with small numbers (negative powers of 10) some pupils may think that the power indicates how many zeros should be placed between the decimal point and the first non-zero digit.

It is almost inevitable in most calculations across the three sciences that decimals will be needed however the most likely places where standard form will occur are:

• In the Cell Biology topic when the size of cells are described.
• In the Chemical Analysis topic in Chemistry where stoichiometric calculations and performed. Calculations involving the mole and Avogadro’s constant are known to be challenging for manty students.
• Speed and motion calculations in physics such as in the Forces and Motion and Light and Electromagnetic waves topics.
• When describing the sizes and distances involved in the Space Physics topic.
• When describing the quantities and sizes of atoms in the Atomic Structure topic in physics, particularly the section on ionizing radiations.