Standard form = one digit, then a power of 10: Standard form (also called scientific notation) writes a number as a Ć 10įµ.
The coefficient a is between 1 and 10. The exponent k is a whole number.
For example, 45 300 = 4.53 Ć 10ā“.
- the coefficient ā one non-zero digit before the decimal point
- the exponent ā an integer (positive, negative or 0)
- Standard form
- A number written as a Ć 10įµ with 1 ā¤ a < 10. Example: 6 Ć 10ā»Ā³.
- Ordinary form
- The everyday way of writing a number. Example: 0.006.
- Coefficient (a)
- The number in front, kept between 1 and 10. Example: the 6 in 6 Ć 10ā»Ā³.
- Exponent (k)
- The power of 10. Example: the ā3 in 6 Ć 10ā»Ā³.
| Ordinary form | Standard form |
|---|---|
| 8 000 | 8 Ć 10Ā³ |
| 453 000 | 4.53 Ć 10āµ |
| 0.006 | 6 Ć 10ā»Ā³ |
| 0.000 21 | 2.1 Ć 10ā»ā“ |
Free preview
This is the free notes preview
You're reading the free notes. Aimnova Pro unlocks the full study experience ā and you can try it with your first topic free to keep:
- FlashcardsLock in vocabulary and key terms with spaced repetition.
- Practice questionsAnswer exam-style questions and get instant AI marking.
- Mock exams & past-paper vaultSit full mocks and see exactly how examiners award marks.
- Personalised study planA daily plan built around your exam date and weak areas.
Two quick steps: 1. Put the decimal point just after the first non-zero digit ā that is a.
2. Count how many places the point moved ā that is k.
For example, 6 040 000 ā 6.04 Ć 10ā¶ (the point moves 6 places).
The rule, with examples
- Big number (10 or more) ā k is positive, the point moves left. For example, 52 000 = 5.2 Ć 10ā“.
- Small number (less than 1) ā k is negative, the point moves right. For example, 0.0007 = 7 Ć 10ā»ā“.
- Always check a is between 1 and 10. For example, 48 = 4.8 Ć 10Ā¹, not 48 Ć 10ā°.
IB-style question ā a big number
Write 45 300 000 in standard form.
Step by step
- Put the point after the first digit to make a coefficient between 1 and 10.
- Count the places the point moved left: 45 300 000 ā 4.53 is 7 places.
- Write them together.
Final answer
45 300 000 = 4.53 Ć 10ā·
IB-style question ā a small number
Write 0.000 64 in standard form.
Step by step
- Put the point after the first non-zero digit (6).
- The point moved 4 places right, so the exponent is negative.
- Write them together.
Final answer
0.000 64 = 6.4 Ć 10ā»ā“
Know your predicted grade
Take timed mock exams and get detailed feedback on every answer. See exactly where you're losing marks.
Common mistake
- 45.3 Ć 10ā¶ ā coefficient too big
- 0.7 Ć 10āµ ā coefficient less than 1
Correct
- 4.53 Ć 10ā·
- 7 Ć 10ā“
- Move the point to just after the first digit
Which paper ā and how it's asked: Paper 1 (no calculator): write a number in standard form by hand, or give a calculated answer in the form a Ć 10įµ.
Paper 2 (calculator): you work out the value on the GDC, then rewrite it in standard form.
Both have appeared on real exams.
Reading the GDC (Paper 2): Your GDC shows big or small numbers using į“. The display 8.58į“3 means 8.58 Ć 10Ā³.
For example, a value shown as 2.1į“-4 is 2.1 Ć 10ā»ā“.
Paper 2 example ā compute, then express
A sphere has radius 9.4 cm.
Find its volume in the form a Ć 10įµ cmĀ³, where 1 ā¤ a < 10.
Step by step
- Use the volume formula and the GDC to work out the value.
- The GDC works out the value.
- Move the point 3 places to write it in standard form.
Final answer
V = 3.48 Ć 10Ā³ cmĀ³ (3 s.f.)
GDC walkthrough
Step through the exact calculator keystrokes, screen by screen, in study mode.
If you see "in the form a Ć 10įµ, 1 ā¤ a < 10": Your final line must have exactly one digit before the decimal point.
For example, finish as 3.6 Ć 10Ā¹Ā³, never 36 Ć 10Ā¹Ā².