Answer the following math questions focusing on significant figures

a. 45.3L x 10 mol/L =
b. 67.894 g ÷ 2.56 L =
c. 45.3m + 12.344m + 1000m – 1.34m =
d. 35cm + 8.3m + 75.341 km + 80,000 mm =
e. (43.7m + 39.3cm) ÷ 25.332 m/s =

To focus on significant figures, we will follow these rules:

1. For multiplication and division, the final answer should have the same number of significant figures as the least precise value used in the calculation.
2. For addition and subtraction, the final answer should have the same number of decimal places as the least precise value used in the calculation.

Let's calculate these step-by-step:

a. 45.3L x 10 mol/L =
- You have one value with three significant figures (45.3 L) and another value with two significant figures (10 mol/L). Since multiplication is involved, we focus on the number of significant figures.
- The least precise value has two significant figures, so the final answer should also have two significant figures.
- 45.3L multiplied by 10 mol/L is 453 mol (both rounded to two significant figures).

b. 67.894 g ÷ 2.56 L =
- You have two values - 67.894 g with four significant figures and 2.56 L with three significant figures. In this case, division is involved, so the least precise value determines the number of significant figures.
- The least precise value has three significant figures, so the final answer should also have three significant figures.
- Dividing 67.894 g by 2.56 L yields an answer of 26.5 g/L (rounded to three significant figures).

c. 45.3m + 12.344m + 1000m – 1.34m =
- You are adding and subtracting values here, so the least precise value determines the number of decimal places.
- All the values are given with three significant figures and units of meters.
- When adding and subtracting these values, the result is 1056.304 meters.

d. 35cm + 8.3m + 75.341 km + 80,000 mm =
- You have values with different units. To perform addition, we need to convert them to the same unit.
- Convert 35 cm to meters: 35 cm ÷ 100 = 0.35 m (two decimal places).
- Convert 80,000 mm to meters: 80,000 mm ÷ 1000 = 80 m (no decimal places).
- Now we have all values in meters: 0.35 m + 8.3 m + 75.341 km + 80 m.
- First, convert 75.341 km to meters: 75.341 km x 1000 = 75341 m (no decimal places).
- Add all the values: 0.35 m + 8.3 m + 75341 m + 80 m = 75329.65 m (rounded to two decimal places).

e. (43.7m + 39.3cm) ÷ 25.332 m/s =
- Convert 39.3 cm to meters: 39.3 cm ÷ 100 = 0.393 m (three decimal places).
- Add the values: 43.7 m + 0.393 m = 44.093 m.
- Then, divide by 25.332 m/s: 44.093 m ÷ 25.332 m/s = 1.741 seconds (rounded to three decimal places).

I hope this helps!

To determine the answers to these math questions while focusing on significant figures, we need to follow specific rules for significant figures. Here are the steps to solve each question:

a. 45.3L x 10 mol/L:
To multiply, we need to determine the number of significant figures in the given values.

- 45.3L: This value has three significant figures.
- 10 mol/L: Since this is a conversion factor, it is considered exact and has an infinite number of significant figures.

To get the answer, we multiply the values and apply the significant figures rules:
45.3L x 10 mol/L = 453 mol

b. 67.894 g ÷ 2.56 L:
To divide, we again need to determine the number of significant figures in the given values.

- 67.894 g: This value has five significant figures.
- 2.56 L: This value has three significant figures.

When dividing, we should round the result to the least number of significant figures:
67.894 g ÷ 2.56 L ≈ 26.5 g/L

c. 45.3m + 12.344m + 1000m – 1.34m:
To add and subtract, we don't have to worry about significant figures; we can simply calculate the sum:

45.3m + 12.344m + 1000m – 1.34m = 1056.304m

d. 35cm + 8.3m + 75.341 km + 80,000 mm:
To add, we need to convert all units to the same unit. Let's convert each of them to meters:

- 35cm = 0.35m (1m = 100cm)
- 8.3m remains the same
- 75.341km = 75341m (1km = 1000m)
- 80,000mm = 80m (1m = 1000mm)

Now we can add the converted values:
0.35m + 8.3m + 75341m + 80m = 75629.65m

e. (43.7m + 39.3cm) ÷ 25.332 m/s:
To divide, we need to convert 39.3cm to meters before performing the calculation:

- 39.3cm = 0.393m (1m = 100cm)

Now we can perform the division:
(43.7m + 0.393m) ÷ 25.332 m/s ≈ 1.72 m/s (rounded to two significant figures)

a. 45.3L x 10 mol/L = 1 sig fig

b. 67.894 g ÷ 2.56 L = 3 sig figs
c. 45.3m + 12.344m + 1000m – 1.34m = answer to the least amount of uncertainty
d. 35cm + 8.3m + 75.341 km + 80,000 mm = answer to the least amount of uncertainty
e. (43.7m + 39.3cm) ÷ 25.332 m/s = 3 sig figs

a. 45.3L x 10 mol/L = 1 sig fig

b. 67.894 g ÷ 2.56 L = 3 sig figs
c. 45.3m + 12.344m + 1000m – 1.34m = answer to the lease amount of uncertainty
d. 35cm + 8.3m + 75.341 km + 80,000 mm = answer to the lease amount of uncertainty
e. (43.7m + 39.3cm) ÷ 25.332 m/s = 3 sig figs