### All ACT Math Resources

## Example Questions

### Example Question #1 : Decimals

When 5/11 is written as a decimal, what is the 100th digit to the right of the decimal point?

**Possible Answers:**

2

4

5

1

0

**Correct answer:**

5

When 5 is divided by 11, the decimal is 0.45 repeating, with a 5 in the hundreths place. The key here is to recognize that 100 is an even number, and the 5 in 0.45 is two places to the right of the decimal point (2 also being an even number).

### Example Question #1 : Decimals

Find the sum of the following:

**Possible Answers:**

**Correct answer:**

To get the decimal from a fraction, divide the numerator by the denominator

### Example Question #2 : Decimals

Find the sum to the nearest hundredth:

**Possible Answers:**

**Correct answer:**

1. Convert the fractions to decimals by division:

2. Add the corresponding whole numbers to the decimals:

3. Add the two decimals:

### Example Question #1 : Decimals

If , can equal which of the following?

**Possible Answers:**

None of the other answer choices are correct

**Correct answer:**

Convert all of the fractions to decimals. Thus, x is contained within the range of 0.33 < x < 0.76. The answers choices become 1/4 = 0.25, 4/12 = 0.33, 2/5 = 0.4, and 5/16 = 0.3125, respectively. Therefore, the only answer which is within the desired range is 2/5.

### Example Question #31 : Decimals With Fractions

Simplify:

**Possible Answers:**

**Correct answer:**

Begin by multiplying all of your decimal fractions by :

Simplify:

Now perform the multiplication:

The easiest thing to do next is to subtract from :

Next, convert into the fraction :

Now, the common denominator can be :

Simplify:

### Example Question #2 : Decimals

Convert 0.825 into a fraction.

**Possible Answers:**

**Correct answer:**

0.825 in fraction form is . Simplifying the fraction equals .

### Example Question #6 : Decimals

What is equivalent to?

**Possible Answers:**

**Correct answer:**

We need to convert into a fraction.

To do this, write down

Now, because the decimal goes to the hundreth place, multiply the numerator and denominator of the fraction by 100.

Now, simplify the fraction.

### Example Question #51 : Decimals

A tub of food contains pounds of vegetables, pounds of lard, and pounds of sausage. What is its total weight as an improper fraction?

**Possible Answers:**

**Correct answer:**

To begin with, it is easiest just to add these decimals together using your calculator:

Now, this is the same thing as:

We can rewrite this:

To find this, you need to give the two numbers a common denominator:

This is your answer.

### Example Question #1 : How To Find The Fractional Equivalent Of A Decimal

What is the fractional equivalent of ?

**Possible Answers:**

**Correct answer:**

In decimal form is said 33 hundredths.

This is equal to

.

This fraction cannot be reduced any further therefore it is in its final answer form.

### Example Question #1 : Decimals

Write 0.45 as a fraction.

**Possible Answers:**

**Correct answer:**

.45 is equivalent to 45 out of 100, or .

Divide both the numerator and denominator by 5 to simplify the fraction: