### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Convert Decimals To Scientific Notation

Write the number 450,000 in scientific notation.

**Possible Answers:**

4.5 x 10^{6}

4.5 x 10^{5}

45 x 10^{5}

45 x 10^{6}

450 x 10^{6}

**Correct answer:**

4.5 x 10^{5}

450,000 = 4.5 x 100,000

100,000 = 10^{5 }(exponent is equal to the number of zeros)

450,000 = 4.5 x 10^{5}

### Example Question #1 : How To Convert Decimals To Scientific Notation

If 3.0147 * 10^{n }= 3,014,700,000, then *n *=

**Possible Answers:**

–8

2

–4

8

9

**Correct answer:**

9

To determine this answer, move the decimal point in 3.0147 until you get 3,014,700,000 (9 places). There are 9 decimal places after the decimal point.

### Example Question #1 : Other Decimals

Write the following number in scientific notation:

**Possible Answers:**

**Correct answer:**

Slide the decimal point to the left as many places as you need to make a number between 1 and 10. Multiply that number by 10 to the power of however many decimal places you moved the decimal.

### Example Question #2 : How To Convert Decimals To Scientific Notation

What is equal to in scientific notation?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Convert Decimals To Scientific Notation

Write in scientific notation.

**Possible Answers:**

**Correct answer:**

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative. If the decimal had moved left, we would have had a positive exponent.

In this case we get 6.009 * 10^{–}^{5}.

### Example Question #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

We need to convert into a number of the form .

The trick is, however, figuring out what should be. When you have to move your decimal point to the *right*, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move *to the left*. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

### Example Question #1 : How To Convert Decimals To Scientific Notation

is equal to which of the following?

**Possible Answers:**

**Correct answer:**

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to .

For each of the answer choices, this would give us:

(Which is, thus, the answer.)

When you convert, you *add* for each place that you move to the *left* and *subtract* for each place you move to the *right*. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

### Example Question #3 : How To Convert Decimals To Scientific Notation

If , what is ?

**Possible Answers:**

**Correct answer:**

This is a bit of a scientific notation application test.

Because is in the ones place , , and because is in the hundredths place , .

From there, it becomes self-explanatory:

.

Remember to take care that you do not give or instead of .

### Example Question #1 : Decimals

Jenny is getting ready for school. She bought school supplies on a tax-free day. She bought notebooks for $1.25 each and crayons for $0.90 each. Jenny bought two more notebooks than crayons. She paid with a ten dollar bill and got $1.05 in change. How many notebooks did she buy?

**Possible Answers:**

5

4

3

2

1

**Correct answer:**

5

Define variables as x = number of crayons and x + 2 = number of notebooks

To find out how much she spent, we subtract her change from what she paid with: 10.00 – 1.05 = 8.95

Then we need to solve the problem cost of notebooks plus the cost of crayons equals the total cost.

1.25(x + 2) + 0.90x = 8.95 and solving for x gives 3 crayons and 5 notebooks

### Example Question #1 : How To Add Decimals

Simplify the following:

**Possible Answers:**

**Correct answer:**

To add decimals, first add zeros to the necessary terms so they all have the same number of places to the right of the decimal point.

Now, temporarily drop the decimal and add the numbers as if they were whole numbers.

Finally, add the decimal place back in, in the same place you removed it from. In this case, we originally modified our numbers so they all had 3 numbers to the right of the decimal, so we will add the decimal back to the exact same place. Thus, our answer is:

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