657800 = 6.578 × 105

OR

657800 = 65.78 × 104

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

2 × 100 + 3 × 102 + 4 × 104 =

2 + 300 + 40,000 = 40,302

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.

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:

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 .

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

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

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: