Curriculum Hub → Maths Lessons → Number → Indices and Standard Form → Introducing Standard Form
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Standard form is one of those topics that looks like new notation but is really just a shortcut for something students already understand: multiplying and dividing by powers of ten. Here’s a lesson approach that builds from that familiar ground, through converting ordinary numbers, and into the exam-style questions students see most often, ordering, converting back, and applying standard form to real-world contexts.
Watch this tutorial first to see how ordinary numbers are converted to standard form. Download the handout to work along with the video, then try the free worksheet below.
Key topics: converting ordinary numbers to standard form, how the power of ten sets the place value of the decimal, and checking answers using the standard form button on a scientific calculator. Download handout.
Download the free worksheet. It includes questions converting numbers bigger and smaller than one to and from standard form, with worked solutions shown in the accordions below.
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At the start of the lesson, students recap multiplying and dividing numbers by a power of ten. Some students may benefit from a place value grid, while others will use mental methods. Students could check their solutions using the ×10ˣ or EXP button on their calculators.
Prompts / Questions to consider
When introducing standard form, discuss how calculations with very big or small numbers become more accessible once they’re written in standard form. After the class discussion, have students work in pairs or small groups to think of five industries that operate with numbers in standard form.
Next, demonstrate how to convert ordinary numbers to standard form, as shown in the video tutorial above.
Students could work through these questions and then progress through the worksheet when ready. Encourage students to check their work using the scientific form button on their scientific calculators.
Prompts / Questions to consider
The plenary includes two common exam-style questions. Have students attempt these on mini-whiteboards so you can assess progress and give feedback. More able students could write the sun’s diameter in cm or mm, and the radius of a hydrogen atom in km.
Prompts / Questions to consider
More able: focus on correcting numbers not currently written in standard form, for example 0.025 × 10⁻¹ becomes 2.5 × 10⁻³.
Less able: additional practice writing numbers bigger than 1 in standard form before moving on to negative powers of ten.
Use this checklist after the lesson or as a revision self-check.
Try these 4 GCSE-style questions, then reveal the solutions to check your working.
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Standard form, also called scientific notation, is a way of writing very large or very small numbers as a number between 1 and 10 multiplied by a power of 10. It makes numbers with many digits much easier to read, compare and calculate with.
Move the decimal point left until only one non-zero digit remains before it, then count how many places the point moved. That count becomes the positive power of 10. For example, 72000 becomes 7.2 times 10 to the power of 4.
Move the decimal point right until only one non-zero digit remains before it, then count how many places the point moved. That count becomes a negative power of 10. For example, 0.0018 becomes 1.8 times 10 to the power of minus 3.
Convert each number back to an ordinary number, or compare the powers of 10 directly once every number is written with a single digit before the decimal point, then order them by size.
Standard form requires the first factor to be between 1 and 10. Since 0.025 is less than 1, it needs to be rewritten as 2.5 times 10 to the power of minus 3 to be in correct standard form.
Standard form is used across science and engineering to handle very large or very small measurements, such as distances in astronomy, the size of atoms, national populations, or amounts of money at a national scale.
Build a coherent indices and standard form unit with these related resources. For the full curriculum, visit the Indices and Standard Form hub.
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