QuestionRound the numbers 2005.0043 and 0.010908 to 3 significant figures and express them in scientific notation.

Studdy Solution

STEP 1

Assumptions1. We are rounding off the numbers to3 significant figures. . We are expressing the answers in scientific notation.

STEP 2

Let's start with the first number,2005.004. To round off this number to significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 3

In this case, the fourth digit after the decimal point is, which is less than5. So, we leave the third digit as it is and remove all the digits after it.
$2005.0043 \approx2005.004$

STEP 4

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 5

Moving the decimal point3 places to the left, we get $2005.004 =2.005 \times10^3$

STEP 6

Now, let's move to the second number,0.010908. To round off this number to3 significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 7

In this case, the fourth digit after the decimal point is9, which is more than5. So, we increase the third digit by one and remove all the digits after it.
$0.010908 \approx0.0109$

STEP 8

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 9

Moving the decimal point2 places to the right, we get $.0109 =.09 \times^{-2}$ So, the numbers2005.0043 and.010908 rounded off to3 significant figures and expressed in scientific notation are $2.005 \times^3$ and $.09 \times^{-2}$ respectively.

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QuestionRound the numbers 2005.0043 and 0.010908 to 3 significant figures and express them in scientific notation.

Studdy Solution

STEP 1

Assumptions1. We are rounding off the numbers to3 significant figures. . We are expressing the answers in scientific notation.

STEP 2

Let's start with the first number,2005.004. To round off this number to significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 3

In this case, the fourth digit after the decimal point is, which is less than5. So, we leave the third digit as it is and remove all the digits after it.
$2005.0043 \approx2005.004$

STEP 4

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 5

Moving the decimal point3 places to the left, we get $2005.004 =2.005 \times10^3$

STEP 6

Now, let's move to the second number,0.010908. To round off this number to3 significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 7

In this case, the fourth digit after the decimal point is9, which is more than5. So, we increase the third digit by one and remove all the digits after it.
$0.010908 \approx0.0109$

STEP 8

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 9

Moving the decimal point2 places to the right, we get $.0109 =.09 \times^{-2}$ So, the numbers2005.0043 and.010908 rounded off to3 significant figures and expressed in scientific notation are $2.005 \times^3$ and $.09 \times^{-2}$ respectively.

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QuestionRound the numbers 2005.0043 and 0.010908 to 3 significant figures and express them in scientific notation.

Studdy Solution

STEP 1

Assumptions1. We are rounding off the numbers to3 significant figures. . We are expressing the answers in scientific notation.

STEP 2

Let's start with the first number,2005.004. To round off this number to significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 3

In this case, the fourth digit after the decimal point is, which is less than5. So, we leave the third digit as it is and remove all the digits after it.2005.0043≈2005.0042005.0043 \approx2005.0042005.0043≈2005.004

STEP 4

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 5

Moving the decimal point3 places to the left, we get2005.004=2.005×1032005.004 =2.005 \times10^32005.004=2.005×103

STEP 6

Now, let's move to the second number,0.010908. To round off this number to3 significant figures, we look at the fourth digit after the decimal point. If this digit is5 or more, we increase the third digit by one. If it's less than5, we leave the third digit as it is.

STEP 7

In this case, the fourth digit after the decimal point is9, which is more than5. So, we increase the third digit by one and remove all the digits after it.0.010908≈0.01090.010908 \approx0.01090.010908≈0.0109

STEP 8

Now, we need to express this number in scientific notation. To do this, we move the decimal point to the right of the first non-zero digit and write the number of places we moved the decimal point as a power of10.

STEP 9

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In this case, the fourth digit after the decimal point is, which is less than5. So, we leave the third digit as it is and remove all the digits after it.
$2005.0043 \approx2005.004$

Moving the decimal point3 places to the left, we get $2005.004 =2.005 \times10^3$

In this case, the fourth digit after the decimal point is9, which is more than5. So, we increase the third digit by one and remove all the digits after it.
$0.010908 \approx0.0109$