### 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:**

45 x 10^{6}

4.5 x 10^{6}

45 x 10^{5}

4.5 x 10^{5}

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 : How To Convert Decimals To Scientific Notation

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 #1 : How To Convert Decimals To Scientific Notation

What is equal to in scientific notation?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Other Decimals

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 #2 : Other Decimals

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 #33 : Decimals

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 .

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