Lesson 10 of 14
Writing a very small number
Show on a big screenA made-up germ is 0.0000025 m (metres) long. Too many zeros to read quickly.
Loading lab…
0.0000025 — a made-up length in metres. Step 1 of 4
0.0000025— a made-up length in metres.- Move the point right. Stop when one digit from 1 to 9 is in front. It moves 6 places.
- The first part is
2.5. The point moved 6, so the exponent is −6. 0.0000025=2.5 × 10⁻⁶.
The rule
Standard form works for small numbers too. Write x × 10ʸ, with x from 1 to below 10. For a number below 1, the exponent y is negative. The count is also called the exponent.
Rule: Move the point right. Stop when x is from 1 to below 10. If it moved k places, the exponent is −k.
The point is the decimal point. Moving it k places right multiplies the number by 10ᵏ. So the exponent is −k, to undo that.
| Number | Point moves | Standard form |
|---|---|---|
| 0.0032 | 3 places | 3.2 × 10⁻³ |
| 0.00047 | 4 places | 4.7 × 10⁻⁴ |
| 0.0000025 | 6 places | 2.5 × 10⁻⁶ |
| 0.5 | 1 place | 5 × 10⁻¹ |
Try the lab to finish this lesson.