0.000319 has □ significant figures.

3. The zeros in front only place the point; they are not significant. Count from the first digit that isn't 0: 3.

What is 0.007738 correct to 3 significant figures? A. 0.00774 B. 0.0077 C. 0.008 D. 0.00773 Choose the right answer

A. 0.00774. Count three figures from 7, the first digit that isn't 0, then look at the fourth, 8: it rounds up. So 0.00774.

494.766 correct to 4 significant figures is □.

494.8. The whole-number part already has three significant figures, so the fourth is the first decimal place; look at the second, 6. So 494.8.

Approximation & estimation · Ages 12–13

Significant figures

Count from the first digit that isn't 0; fill whole numbers with zeros.

How to do it

Method

Count from the first digit that isn't 0; fill whole numbers with zeros

0.004070 has 4 s.f.; 34,567 ≈ 35,000 (2 s.f.)

Another way

As digits times a power of 10

0.004070 = 4.070 × 0.001: 4 figures

In full

The first significant figure is the first digit from the left that isn't 0. Zeros in front only place the point and are not significant: 0.00407 has 3 significant figures (4, 0 and 7). A zero between other digits is significant, and so is a zero at the end after the decimal point: 0.004070 has 4 significant figures, its last 0 saying it is correct to the millionth. To 3 significant figures: count three significant digits, look at the next, and round off. Fill the whole-number places with zeros to keep their values: 34,567 to 2 s.f. is 35,000, not 35. Compare decimal places: 0.004070 to 2 d.p. is 0.00, but to 2 s.f. it is 0.0041. Or write the number as digits times a power of 10 first: 0.004070 = 4.070 × 0.001, and 4.070 has four digits.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
0.000319 has significant figures.
Show the answer and working
Answer: 3
The zeros in front only place the point; they are not significant. Count from the first digit that isn't 0: 3.
Example 2
What is 0.007738 correct to 3 significant figures?
- A. 0.00774
- B. 0.0077
- C. 0.008
- D. 0.00773
Choose the right answer
Show the answer and working
Answer: A. 0.00774
Count three figures from 7, the first digit that isn't 0, then look at the fourth, 8: it rounds up. So 0.00774.
Example 3
494.766 correct to 4 significant figures is .
Show the answer and working
Answer: 494.8
The whole-number part already has three significant figures, so the fourth is the first decimal place; look at the second, 6. So 494.8.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.0.0239 has 5 significant figures.
True or false?
Answer:
2.Which number has exactly 3 significant figures?
- A. 0.00908
- B. 0.9080
- C. 0.00098
- D. 90.08
Choose the right answer
Answer:
3.0.000376 has significant figures.
Answer:
4.What is 0.009389 correct to 3 significant figures?
- A. 0.0094
- B. 0.009
- C. 0.00938
- D. 0.00939
Choose the right answer
Answer:
5.373.672 correct to 4 significant figures is .
Answer:

All the answers

1. False
2. A. 0.00908
3. 3
4. D. 0.00939
5. 373.7

Free worksheet: Significant figuresWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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