### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Use Scientific Notation

What is the sum of the solutions of the equation x^{2}-2x-8=0?

**Possible Answers:**

-10

-6

6

-2

2

**Correct answer:**

2

The equation factors to (x-4)(x+2)=0, indicating that the roots are x=-2,4. The sum of these two roots is 2.

### Example Question #1 : Other Exponents

What is the number 350,000,000 in scientific notation?

**Possible Answers:**

3.5 x 10^{6}

3.5 x 10^{5}

3.5 x 10^{7}

3.5 x 10^{9}

3.5 x 10^{8}

**Correct answer:**

3.5 x 10^{8}

350,000,000 = 3.5 x 10^{8 }(exponent is equal to the number of decimal points shifted)

### Example Question #3 : How To Use Scientific Notation

Given the equation 2xy + 4x² - y = 2x, if x = 2, what does y equal?

**Possible Answers:**

4

-4

2

0

**Correct answer:**

-4

We plug in the value given for x and solve for y.

2xy + 4x² - y = 2x

2(2)y + 4(2)² - y = 2(2)

4y + 4(4) - y = 4

4y - y + 16 = 4

3y = -12

y = -4

### Example Question #1 : How To Use Scientific Notation

How do you express 657,800 in scientific notation?

**Possible Answers:**

65.78 × 10^{3}

65.78 × 10^{4}

65.78 × 10^{6}

6.578 × 10^{3}

6.578 × 10^{4}

**Correct answer:**

65.78 × 10^{4}

657800 = 6.578 × 10^{5}

OR

657800 = 65.78 × 10^{4}

Exponent on 10 is the number of decimal points over the number has shifted.

### Example Question #5 : How To Use Scientific Notation

2 × 10^{0} + 3 × 10^{2} + 4 × 10^{4} = ?

**Possible Answers:**

4,032

40,320

40,302

400,032

432

**Correct answer:**

40,302

2 × 10^{0} + 3 × 10^{2} + 4 × 10^{4} =

2 + 300 + 40,000 = 40,302

### Example Question #1 : How To Use Scientific Notation

Give this number in scientific notation:

**Possible Answers:**

**Correct answer:**

There are six zeros and two more number places, for a total of eight, so 125,000,000 is equivalent to .

### Example Question #7 : How To Use Scientific Notation

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Use Scientific Notation

What is the number in scientific notation?

**Possible Answers:**

**Correct answer:**

The exponent is equal to the number of decimal points shifted.

### Example Question #1 : How To Use Scientific Notation

Convert from scientific to decimal notation:

**Possible Answers:**

**Correct answer:**

In this case the exponent is positive hence you have to move the decimal point 4 places to the right from where it is in the problem giving us

### Example Question #2 : Other Exponents

Convert from decimal to scientific notation:

**Possible Answers:**

**Correct answer:**

In this case you have to move the decimal point 6 places to the right. When you move the decimal point to the right the exponent becomes negative. Similarly when you move the decimal point to the left the exponent is positive. Also, to the left of the decimal place there can be only one digit.