Scientific notation is used to simplify exceptionally complex numbers and to quickly present the number of significant figures in a given value. The value is converted to an exponent form using base ten, such that only a single-digit term with any given number of decimal places is used to represent the significant figures of the given value. Non-significant zeroes can be omitted from the leading term, and represented only in the base ten exponent.

The given number has five significant figures (100.43), so there will be five digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 1 (1.0043). Then count the digits to the right of the decimal to determine the change in decimal placement (the decimal moves past the two zeroes). Our ten will be raised to the power of two because there are two digits to the right of the final decimal placement.

Our final answer is

Scientific notation is used to simplify exceptionally complex numbers and to quickly present the number of significant figures in a given value. The value is converted to an exponent form using base ten, such that only a single-digit term with any given number of decimal places is used to represent the significant figures of the given value. Non-significant zeroes can be omitted from the leading term, and represented only in the base ten exponent.

The given number has five significant figures (100.43), so there will be five digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 1 (1.0043). Then count the digits to the right of the decimal to determine the change in decimal placement (the decimal moves past the two zeroes). Our ten will be raised to the power of two because there are two digits to the right of the final decimal placement.

Our final answer is

Any time we write a number in scientific notation, we want to keep the same number of significant figures, but have the decimal end up where it was in the original number. For the number 13,200, we have 3 significant figures: 1,3, & 2. So right now what we have is 132; our next step is to insert a decimal somewhere on 132 that would turn it into a number between 1-10. We are left with 1.32 To get to 1.32, we have to move the nonexhistent decimal from the end of 13200 four places to the left. Anytime we move decimals to the left, the exponent in scientific notation gets larger.

Any time we write a number in scientific notation, we want to keep the same number of significant figures, but have the decimal end up where it was in the original number. For the number 13,200, we have 3 significant figures: 1,3, & 2. So right now what we have is 132; our next step is to insert a decimal somewhere on 132 that would turn it into a number between 1-10. We are left with 1.32 To get to 1.32, we have to move the nonexhistent decimal from the end of 13200 four places to the left. Anytime we move decimals to the left, the exponent in scientific notation gets larger.

When performing addition or subtraction in chemistry you can only be as precise as the number with the fewest number of decimal not significant figures. Because only has 1 decimal place the answer of the addition problem can only have 1 decimal place. All of the other numbers have more than 1 decimal place so that is why the other answers are incorrect.

When performing addition or subtraction in chemistry you can only be as precise as the number with the fewest number of decimal not significant figures. Because only has 1 decimal place the answer of the addition problem can only have 1 decimal place. All of the other numbers have more than 1 decimal place so that is why the other answers are incorrect.

Let's look at the rules of significant figures:

I. All nonzero digits are significant.

II. Any zero found anywhere between nonzero digits is significant.

III. Any zero to the right of the decimal point AND after a nonzero digit is significant.

IV. Any zero to the left of the decimal point AND after a nonzero digit is significant. Any zero found after a nonzero digit with no decimal point indication is NOT significant.

Rule I gives us only one nonzero significant figure. However, rule IV tells us that the zeroes are significant because there is a decimal present and the zeroes are following a nonzero digit. Therefore, has four significant figures.

Let's look at the rules of significant figures:

I. All nonzero digits are significant.

II. Any zero found anywhere between nonzero digits is significant.

III. Any zero to the right of the decimal point AND after a nonzero digit is significant.

IV. Any zero to the left of the decimal point AND after a nonzero digit is significant. Any zero found after a nonzero digit with no decimal point indication is NOT significant.

Rule I gives us only one nonzero significant figure. However, rule IV tells us that the zeroes are significant because there is a decimal present and the zeroes are following a nonzero digit. Therefore, has four significant figures.

Converting a value from scientific notation to standard notation is a simple matter of multiplication.

Since we are always multiplying by a base ten term, the value of the exponent determines the increase/decrease in terms of orders of magnitude. In this case, an exponent of 4 indicates a four-fold increase in order of magnitude. Some may find it easiest to determine the answer by simply adjusting the decimal four digits to the right, adding zeroes as necessary.

Whether you choose to multiply or to simply shift the decimal, the final answer will be .

Numbers in scientific notation must be written with the first number .

How ever many decimal places that you have to move your number to the right the exponent is positive. If you have to move the decimal point to the left to get your number the exponent is negative.

The number is . You would first write this number as , move the decimal point 6 places to the right to obtain your number thus the exponent is