Standard Form
Write very large and very small numbers as a number between 1 and 10 times a power of ten, and calculate with them by hand and on a calculator.
What a learner can do afterwards
- Convert between ordinary numbers and standard form in both directions
- Multiply and divide in standard form using the index laws
- Correct an answer such as 34 × 10⁵ that is not yet in standard form
1 · Read
Standard form writes a number as a leader between 1 and 10 times a power of 10. 5,600,000 becomes 5.6 times 10^6 because the point moves 6 places. Small numbers use negative powers: 4.7 times 10^-4 is 0.00047.
Calculating splits into two easy jobs: leaders together, powers together. (2 times 10^3) times (3 times 10^4): 2 times 3 = 6, powers add 3 + 4 = 7, giving 6 times 10^7. Division mirrors it: (8 times 10^6) divided by (2 times 10^2) is 4 times 10^4.
If the leader drifts out of range, fix it before you finish. 34 times 10^5 is not standard form because 34 exceeds 10: split 34 into 3.4 times 10, then merge powers to get 3.4 times 10^6. The same repair rescues tiny leaders below 1. Always check the leader sits between 1 and 10.
Count places, not zeros, when you convert back: positive powers grow, negative powers shrink. This final tidy-up is where most marks hide, so never hand in a leader outside 1 to 10.
Leader between 1 and 10, powers add or subtract, then fix any drifting leader.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.