Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. your calculator answer would be 11.76 cm2. now suppose you are asked to enter the answer to two significant figures. (note that if you do not round your answer to two significant figures, your answer will fall outside of the grading tolerance and be graded as incorrect.)

The area of the rectangle is 12 cm² ⇒ in 2 significant figures

Step-by-step explanation:

* Lets talk about the significant figures

- All non-zero digits are significant

# 73 has two significant figures

- Zeroes between non-zeros digits are significant

# 105.203 has six significant figures

- Leading zeros are never significant

# 0.00234 has three significant figures

- In a number with a decimal point, zeros to the right of the last

 non-zero digit are significant

# 19.00 has four significant figures

- Lets make a number and then approximate it to different significant

∵ 12.7360 has 6 significant figures

∴ 12.736 ⇒ approximated to 5 significant figures

∴ 12.74 ⇒ approximated to 4 significant figures

∴ 12.7 ⇒ approximated to 3 significant figures

∴ 13 ⇒ approximated to 2 significant figures

∴ 10 ⇒ approximated to 1 significant figure

- Another number with decimal point

∵ 0.0546700 has 6 significant figures

∴ 0.054670 ⇒ approximated to 5 significant figures

∴ 0.05467 ⇒ approximated to 4 significant figures

∴ 0.0547 ⇒ approximated to 3 significant figures

∴ 0.055 ⇒ approximated to 2 significant figures

∴ 0.05 ⇒ approximated to 1 significant figures

* Lets solve the problem

∵ The width of the rectangle is 2.1 cm

∵ The length of the rectangle is 5.6 cm

- Area of the rectangle = length × width

∴ Area of the rectangle = 2.1 × 5.6 = 11.76 cm²

- Approximate it to two significant figures

∴ Area of the rectangle = 12 ⇒ to the nearest 2 significant figures

* The area of the rectangle is 12 cm² ⇒ in 2 significant figures