How to use scientific notation - ACT Math

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.

2 × 100 + 3 × 102 + 4 × 104 =

2 + 300 + 40,000 = 40,302

657800 = 6.578 × 105

OR

657800 = 65.78 × 104

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

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

350,000,000 = 3.5 x 108 (exponent is equal to the number of decimal points shifted)

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

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.

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

First, when we round to the nearest thousand we get 5, 679, 000 since we round up when the next digit is greater than 5.

Then, to put it in scientific notation, we arrange the digits so that a decimal point creates a number between 1 and 10. We get 5.679.

Then, we want the exponent of the 10 to be the number of times the decimal needs to move to the right. This is 6 times.

Thus, we get our answer.

In order to write a number in scientific notation, you must shift the number of decimal places to get a number in the ones place.

Since the original number is a decimal, the exponent will need to be negative. This eliminates three answer choices.

In order to get into scientific notation with '5' in the ones place, you must shift the decimal over seven places.

Therefore, the final answer in scientific notation is .

The easiest way to solve a question like this is to convert the answers all into easily comparable numbers. Remember that you move the decimal place to the left for negative powers of and to the right for positive powers. Thus, for your number, you have:

Notice that the negative power has no influence on the sign of the number. This allows you to eliminate the negative options. The correct answer is:

When you move the decimal places to the right, you also get:

The easiest way to work with a large number like this is to combine the factors and then the other coefficients. After that, you will have to convert the number into scientific notation to match the answer:

Combine the powers of :

Next, combine the other coefficients:

Now, rewrite the leading number like this:

Thus, you get:

For this, you can handle the s separately from the coefficients. The s easily cancel:

Now, handle the coefficients like they are a separate fraction:

Notice, though, that :

Now, you need to get this into scientific notation for your answer. It is easiest ot think of it like this: