Scientific Notation and Significant Figures - AP Chemistry

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 only one significant figure (), so there will only be one digit multiplied by the base ten term.

There are two non-significant zeroes, so our ten will be raised to the power of two.

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 four significant figures (3123), so there will be four digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the first 3. Then count the digits to the right of the decimal (123). Our ten will be raised to the power of three.

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 only one significant figure (), so there will only be one digit multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 4. Then count the digits to the left of the decimal (moving from right to left, these are and ). Our ten will be raised to the power of negative two because there are two digits to the left 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 three significant figures (321), so there will be three digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 3 (3.21). Then count the digits to the left of the decimal (moving from right to left, these are 3, 0, 0). Our ten will be raised to the power of negative three because there are three digits to the left 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

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 three significant figures (60.1), so there will be three digits multiplied by the base ten term.

To generate the single-digit leading term the decimal must be placed after the 6 (6.01). Then count the digits to the right of the decimal to determine the change in decimal placement (the decimal moves past the zero only). Our ten will be raised to the power of one because there is only one digit to the right of the final decimal placement.

Our final answer is

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 .

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 indicates a four-fold decrease in order of magnitude. Some may find it easiest to determine the answer by simply adjusting the decimal four digits to the left, adding zeroes as necessary.

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

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.

We are told that the final value must have four significant figures, so there will be four digits multiplied by the base ten term. Since the given value has only one significant figure, we will need to add three zeroes (4000).

To generate the single-digit leading term the decimal must be placed after the 4 (4.000). Then count the digits to the right of the decimal to determine the change in decimal placement (the decimal moves past three zeroes). Our ten will be raised to the power of three because there are three 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.

We are told that the final value must have four significant figures, so there will be four digits multiplied by the base ten term. Since the given value has only three significant figures, we will need to add a zero (2310).

To generate the single-digit leading term the decimal must be placed after the 2 (2.310). Then count the digits to the left of the decimal to determine the change in decimal placement (the decimal moves past three zeroes and the 2). Our ten will be raised to the power of negative four because there are four digits to the left 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.

We are told that the final value must have four significant figures, so there will be four digits multiplied by the base ten term. We take only the first four digits, rounding the final digit depending on the final term; in this case we round up (3219).

To generate the single-digit leading term the decimal must be placed after the 3 (3.219). Then count the digits to the right of the decimal based on the original value to determine the change in decimal placement (the decimal moves past the following digits in the original term: 128941207). Our ten will be raised to the power of nine because there are nine 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.

We are told that the final value must have six significant figures, so there will be six digits multiplied by the base ten term. We take only the first six digits, rounding the final digit depending on the final term; in this case we round up (123457).

To generate the single-digit leading term the decimal must be placed after the 1 (1.23457). Then count the digits to the left of the decimal to determine the change in decimal placement (the decimal moves past the 1 only). Our ten will be raised to the power of negative one because there is only one digit to the left of the final decimal placement.

Our final answer is .

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

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.

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.

If we apply rule I, the answer should be two significant figures since is a two-digit number.

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.

Let's look at rule I first. In , there are two nonzero digits. According to rule II, the zero is significant as well. has three 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.

Let's look at rule I. only has one nonzero digit, and two zeroes. So far, there's one significant digit. There is no decimal point present, so according to rule IV the zeroes are insignificant. only has one significant figure.

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.

Let's look at rule I. In , there is only one nonzero digit and two zeroes present. That gives us one significant figure. Now, looking at rule III, the zero is to the right of the decimal but there is no nonzero digit to the left of it, making the leading zero insignificant. Finally, in rule IV, the zero after the decimal point is before the nonzero digit making and is also insignificant.

contains only one significant figure.

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.

According to rule I, the two nonzero digits will be significant. The zeroes can be classified under rule II, as they all fall between two nonzero digits (the presence of the decimal here is negligible). The result is five sigificant figures in the given number, .

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 three significant figures, as there are three nonzero digits. Next, there are two zeroes positioned between two nonzero digits; these are both significant according to rule II . The zero to the right of the three obeys rule III and must be significant. All six of the digits in are significant.