science math skills
22. write 0.00045 in scientific notation.
23. write 3.2 × 10⁴ in standard form.
24. in a sample, the ratio of red flowers to white flowers is 3:5. if there are 15 red flowers, how many white flowers are there?
25. a solution has a ratio of 2 g of solute per 100 ml of solvent. how many grams of solutes are needed for 300 ml?
26. a student calculates density but forgets to include units.
a. explain why units are important in science calculations.
27. two students calculate percent change using different methods but get different answers.
a. list one common mistake that could cause this.
28. a scientist is preparing a saline solution for an experiment. the total mass of the solution is 250 grams. the mass of the salt used is 40 grams. let x represent the mass of the water in the solution.
a. write and solve an equation to find the value of x.

Question

science math skills
22. write 0.00045 in scientific notation.
23. write 3.2 × 10⁴ in standard form.
24. in a sample, the ratio of red flowers to white flowers is 3:5. if there are 15 red flowers, how many white flowers are there?
25. a solution has a ratio of 2 g of solute per 100 ml of solvent. how many grams of solutes are needed for 300 ml?
26. a student calculates density but forgets to include units.
    a. explain why units are important in science calculations.
27. two students calculate percent change using different methods but get different answers.
    a. list one common mistake that could cause this.
28. a scientist is preparing a saline solution for an experiment. the total mass of the solution is 250 grams. the mass of the salt used is 40 grams. let x represent the mass of the water in the solution.
    a. write and solve an equation to find the value of x.

Accepted Answer

### Question 22
# Explanation:
## Step1: Identify the coefficient and exponent
To write a number in scientific notation, we use the form $ a \times 10^n $, where $ 1 \leq |a| < 10 $ and $ n $ is an integer. For $ 0.00045 $, we move the decimal point to the right until we get a number between 1 and 10. We move it 4 places to the right, so $ a = 4.5 $ and $ n=-4 $ (since we moved the decimal to the right, $ n $ is negative).
## Step2: Write in scientific notation
Using the form $ a \times 10^n $, we have $ 0.00045 = 4.5 \times 10^{-4} $.
# Answer:
$ 4.5 \times 10^{-4} $

### Question 23
# Explanation:
## Step1: Understand the exponent
In scientific notation $ 3.2 \times 10^4 $, the exponent $ 4 $ means we move the decimal point 4 places to the right (since the exponent is positive).
## Step2: Move the decimal point
Starting with $ 3.2 $, moving the decimal point 4 places to the right gives $ 32000 $.
# Answer:
$ 32000 $

### Question 24
# Explanation:
## Step1: Set up the proportion
The ratio of red to white flowers is $ 3:5 $. Let $ x $ be the number of white flowers. We know there are 15 red flowers, so we set up the proportion $ \frac{3}{5}=\frac{15}{x} $.
## Step2: Cross - multiply and solve
Cross - multiplying gives $ 3x = 15\times5 $. Then $ 3x = 75 $. Dividing both sides by 3, we get $ x=\frac{75}{3}=25 $.
# Answer:
25

### Question 25
# Explanation:
## Step1: Set up the ratio
The ratio of solute to solvent is $ 2\space g:100\space mL $. Let $ x $ be the mass of solute for $ 300\space mL $ of solvent. We set up the proportion $ \frac{2}{100}=\frac{x}{300} $.
## Step2: Cross - multiply and solve
Cross - multiplying gives $ 100x = 2\times300 $. Then $ 100x = 600 $. Dividing both sides by 100, we get $ x = 6 $.
# Answer:
6 grams

### Question 26a
# Brief Explanations:
Units are important in science calculations because they provide context about the quantity being measured. For example, a density value of "5" is meaningless without units, but "5\space g/cm^3" tells us it is 5 grams per cubic centimeter. Units also help in checking the validity of calculations (dimensional analysis) and in communicating results clearly to others in the scientific community.
# Answer:
Units provide context for measured quantities, enable dimensional analysis to check calculation validity, and ensure clear communication of results.

### Question 27a
# Brief Explanations:
One common mistake is using the wrong base value for the percent change formula. The percent change formula is $ \text{Percent Change}=\frac{\text{New Value}-\text{Old Value}}{\text{Old Value}}\times100\% $. If one student uses the new value as the denominator (instead of the old value) or miscalculates the difference between the new and old values, it can lead to different answers. Another mistake could be miscalculating the difference (e.g., subtracting old from new instead of new from old or vice - versa in a wrong context) or using the wrong values for new and old.
# Answer:
Using the wrong base (denominator) in the percent - change formula (e.g., using new value instead of old value) or miscalculating the difference between new and old values.

### Question 28a
# Explanation:
## Step1: Write the equation
The total mass of the solution is the sum of the mass of salt and the mass of water. The total mass of the solution is 250 grams, the mass of salt is 40 grams, and the mass of water is $ x $ grams. So the equation is $ 40 + x=250 $.
## Step2: Solve the equation
Subtract 40 from both sides of the equation: $ x = 250 - 40 $. So $ x = 210 $.
# Answer:
The equation is $ 40 + x = 250 $ and $ x = 210 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Question 22

Step1: Identify the coefficient and exponent

Step2: Write in scientific notation

Step1: Understand the exponent

Step2: Move the decimal point

Step1: Set up the proportion

Step2: Cross - multiply and solve

Answer:

Question 23