Question

summary of rules for determining significant figures (sf).

• numbers determined by counting have an infinite number of significant digits. e.g., i own 3 dogs, exactly.
• numbers that are part of a definition have an infinite number of significant digits. e.g., 1 m = 100 cm, exactly
• any non - zero digit is significant, e.g., 45.8 kg has 3 sf.
• zeroes between non - zero digits are significant, e.g., 8704 km has 4 sf.
• zeroes to the left of non - zero digits are not significant, e.g., 0.0035 mg has 2 sf.
• zeroes to the right of the last non - zero digit and to the right of the decimal place are significant, e.g., 2.350 l has 4 sf.
• zeroes to the right of the last non - zero digit and are to the left of the decimal are ambiguous and are considered not significant, e.g., 350 j has 2 sf.

rules for rounding
use the following three rules for rounding numbers:

1. when adding or subtracting numbers, round the result to the same number of decimal places as the number with the least number of decimal places.

56.8 g + 9.021 g =
35.45°c - 7.9°c =

1. when multiplying or dividing numbers, round the result to the same number of digits as the number with the least number of significant figures.

57.3 x 0.7575 =
83.0034/3.7 =

1. if the digit to be dropped is less than 5,

ound down\ and if it is more than 5,
ound up\. if the dropped digit is exactly 5, round up if the preceding number is odd, and round down if the preceding digit is even. if any nonzero digits follow the dropped 5, round up.
round the following to 1 decimal place:
85.4500
85.45061
85.5500

Explanation:

Step1: Add values first

$56.8\ \text{g} + 9.021\ \text{g} = 65.821\ \text{g}$

Step2: Round to 1 decimal place

Round $65.821$ to 1 decimal place: $65.8\ \text{g}$

Step3: Subtract values first

$35.45^\circ\text{C} - 7.9^\circ\text{C} = 27.55^\circ\text{C}$

Step4: Round to 1 decimal place

Round $27.55$ to 1 decimal place: $27.6^\circ\text{C}$

Step5: Multiply values first

$57.3 \times 0.7575 = 43.30475$

Step6: Round to 3 significant figures

Round $43.30475$ to 3 SF: $43.3$

Step7: Divide values first

$83.0034 \div 3.7 \approx 22.433351$

Step8: Round to 2 significant figures

Round $22.433351$ to 2 SF: $22$

Step9: Round 85.4500 to 1 decimal

Dropped digit=5, preceding digit=4 (even): $85.4$

Step10: Round 85.45061 to 1 decimal

Dropped digit=5 with non-zero digits after: $85.5$

Step11: Round 85.5500 to 1 decimal

Dropped digit=5, preceding digit=5 (odd): $85.6$

Answer:

1. $56.8\ \text{g} + 9.021\ \text{g} = 65.8\ \text{g}$
2. $35.45^\circ\text{C} - 7.9^\circ\text{C} = 27.6^\circ\text{C}$
3. $57.3 \times 0.7575 = 43.3$
4. $83.0034 \div 3.7 = 22$
5. Rounded values to 1 decimal place:

• $85.4500 = 85.4$
• $85.45061 = 85.5$
• $85.5500 = 85.6$