# ACT Math : Decimals

## Example Questions

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### Example Question #1 : Decimals

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

0

4

2

5

1

5

Explanation:

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 #1087 : Hspt Mathematics

Find  the sum of the following:

Explanation:

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

### Example Question #2 : Decimals

Find the sum to the nearest hundredth:

Explanation:

1. Convert the fractions to decimals by division:

2. Add the corresponding whole numbers to the decimals:

### Example Question #3 : Decimals

If can equal which of the following?

None of the other answer choices are correct

Explanation:

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 #4 : Decimals

Simplify:

Explanation:

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 #5 : Decimals

Convert 0.825 into a fraction.

Explanation:

0.825 in fraction form is .  Simplifying the fraction equals .

### Example Question #6 : Decimals

What is  equivalent to?

Explanation:

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

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

Explanation:

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:

### Example Question #8 : Decimals

What is the fractional equivalent of ?

Explanation:

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 #2051 : Psat Mathematics

Write 0.45 as a fraction.