QuestionCount the significant digits in these measurements: $6.8 \times 10^{-1} \mathrm{~mL}$ , $80500 \mathrm{~kg}$ , $4.0 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol}$ , $0.00300 \mathrm{~J}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are given in scientific notation or standard form. . We are counting the significant digits, which are digits from the first non-zero digit to the last non-zero digit in the number, including any zeroes in between.

STEP 2

Let's start with the first measurement $6.8 \times10^{-1} \mathrm{~m}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 3

In the number $6.8$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 4

Count the number of significant digits in $6.8$ .
There are2 significant digits in $6.8$ .

STEP 5

Now, let's move on to the second measurement $80500 . \mathrm{kg}$ . Again, the significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 6

In the number $80500$ , there are trailing zeros without a decimal point, which are not considered significant.

STEP 7

Count the number of significant digits in $80500$ .
There are3 significant digits in $80500$ .

STEP 8

Next, let's consider the third measurement $4.0 \times10^{-3} \mathrm{~kJ} / \mathrm{mol}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 9

In the number $4.$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 10

Count the number of significant digits in $4.0$ .
There are2 significant digits in $4.0$ .

STEP 11

Finally, let's consider the fourth measurement $0.00300 \mathrm{~J}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 12

In the number $0.00300$ , there are leading zeros which are not considered significant. However, trailing zeros in a number with a decimal point are considered significant.

STEP 13

Count the number of significant digits in $0.00300$ .
There are3 significant digits in $0.00300$ .
So, the number of significant digits in each measurement are\begin{tabular}{|c|c|} \hline measurement & $\begin{array}{c}\text { number of } \\ \text { significant } \\ \text { digits }\end{array}$ \\ \hline $6.8 \times10^{-} \mathrm{~m}$ & $2$ \\ \hline $80500 . \mathrm{kg}$ & $3$ \\ \hline $.0 \times10^{-3} \mathrm{~kJ} / \mathrm{mol}$ & $2$ \\ \hline $0.00300 \mathrm{~J}$ & $3$ \\ \hline\end{tabular}

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QuestionCount the significant digits in these measurements: $6.8 \times 10^{-1} \mathrm{~mL}$ , $80500 \mathrm{~kg}$ , $4.0 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol}$ , $0.00300 \mathrm{~J}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are given in scientific notation or standard form. . We are counting the significant digits, which are digits from the first non-zero digit to the last non-zero digit in the number, including any zeroes in between.

STEP 2

Let's start with the first measurement $6.8 \times10^{-1} \mathrm{~m}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 3

In the number $6.8$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 4

Count the number of significant digits in $6.8$ .
There are2 significant digits in $6.8$ .

STEP 5

Now, let's move on to the second measurement $80500 . \mathrm{kg}$ . Again, the significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 6

In the number $80500$ , there are trailing zeros without a decimal point, which are not considered significant.

STEP 7

Count the number of significant digits in $80500$ .
There are3 significant digits in $80500$ .

STEP 8

Next, let's consider the third measurement $4.0 \times10^{-3} \mathrm{~kJ} / \mathrm{mol}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 9

In the number $4.$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 10

Count the number of significant digits in $4.0$ .
There are2 significant digits in $4.0$ .

STEP 11

Finally, let's consider the fourth measurement $0.00300 \mathrm{~J}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 12

In the number $0.00300$ , there are leading zeros which are not considered significant. However, trailing zeros in a number with a decimal point are considered significant.

STEP 13

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QuestionCount the significant digits in these measurements: 6.8×10−1 mL6.8 \times 10^{-1} \mathrm{~mL}6.8×10−1 mL, 80500 kg80500 \mathrm{~kg}80500 kg, 4.0×10−3 kJ/mol4.0 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol}4.0×10−3 kJ/mol, 0.00300 J0.00300 \mathrm{~J}0.00300 J.

Studdy Solution

STEP 1

Assumptions1. The numbers are given in scientific notation or standard form. . We are counting the significant digits, which are digits from the first non-zero digit to the last non-zero digit in the number, including any zeroes in between.

STEP 2

Let's start with the first measurement 6.8×10−1 m6.8 \times10^{-1} \mathrm{~m}6.8×10−1 m. The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 3

In the number 6.86.86.8, there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 4

Count the number of significant digits in 6.86.86.8.There are2 significant digits in 6.86.86.8.

STEP 5

Now, let's move on to the second measurement 80500.kg80500 . \mathrm{kg}80500.kg. Again, the significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 6

In the number 805008050080500, there are trailing zeros without a decimal point, which are not considered significant.

STEP 7

Count the number of significant digits in 805008050080500.There are3 significant digits in 805008050080500.

STEP 8

Next, let's consider the third measurement 4.0×10−3 kJ/mol4.0 \times10^{-3} \mathrm{~kJ} / \mathrm{mol}4.0×10−3 kJ/mol. The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 9

In the number 4.4.4., there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

STEP 10

Count the number of significant digits in 4.04.04.0.There are2 significant digits in 4.04.04.0.

STEP 11

Finally, let's consider the fourth measurement 0.00300 J0.00300 \mathrm{~J}0.00300 J. The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

STEP 12

In the number 0.003000.003000.00300, there are leading zeros which are not considered significant. However, trailing zeros in a number with a decimal point are considered significant.

STEP 13

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QuestionCount the significant digits in these measurements: $6.8 \times 10^{-1} \mathrm{~mL}$ , $80500 \mathrm{~kg}$ , $4.0 \times 10^{-3} \mathrm{~kJ} / \mathrm{mol}$ , $0.00300 \mathrm{~J}$ .

Let's start with the first measurement $6.8 \times10^{-1} \mathrm{~m}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

In the number $6.8$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

Count the number of significant digits in $6.8$ .
There are2 significant digits in $6.8$ .

Now, let's move on to the second measurement $80500 . \mathrm{kg}$ . Again, the significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

In the number $80500$ , there are trailing zeros without a decimal point, which are not considered significant.

Count the number of significant digits in $80500$ .
There are3 significant digits in $80500$ .

Next, let's consider the third measurement $4.0 \times10^{-3} \mathrm{~kJ} / \mathrm{mol}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

In the number $4.$ , there are no leading zeros, trailing zeros, or placeholder zeros. Therefore, all digits are significant.

Count the number of significant digits in $4.0$ .
There are2 significant digits in $4.0$ .

Finally, let's consider the fourth measurement $0.00300 \mathrm{~J}$ . The significant digits are all the digits in the number excluding any leading zeros, trailing zeros in a number without a decimal point, and any zeros that are placeholders.

In the number $0.00300$ , there are leading zeros which are not considered significant. However, trailing zeros in a number with a decimal point are considered significant.