QuestionCount the significant digits in these measurements: $-8.0 \times 10^{-1} \mathrm{~kJ/mol}$ , $0.007500 \mathrm{~J}$ , $3.3 \times 10^{-3} \mathrm{~mL}$ , $40400 \mathrm{~kg}$ .

Studdy Solution

STEP 1

Assumptions1. We are counting the significant digits in each measurement. . The rules for counting significant digits are as follows - All non-zero digits are significant. - Any zeros between significant digits are significant. - Leading zeros are not significant. - Trailing zeros are significant only if they are after a decimal point.

STEP 2

Let's start with the first measurement, $-8.0 \times10^{-1} \mathrm{~kJ} / \mathrm{mol}$ .
The significant digits are the digits in the number that carry meaningful information about its precision. In scientific notation, all the digits in the mantissa (the part before the exponent) are significant. Here, the mantissa is $-8.0$ .

STEP 3

Count the significant digits in $-8.0$ .
There are two significant digits8 and0. The zero is significant because it is a trailing zero that comes after a decimal point.

STEP 4

The number of significant digits in $-8.0 \times10^{-1} \mathrm{~kJ} / \mathrm{mol}$ is2.

STEP 5

Next, let's look at the second measurement, $0.007500 \mathrm{~J}$ .

STEP 6

Count the significant digits in $0.007500$ .
The leading zeros are not significant. The four digits after the leading zeros (,5,0, and0) are all significant. The zeros are significant because they are trailing zeros that come after a decimal point and a non-zero digit.

STEP 7

The number of significant digits in $0.007500 \mathrm{~J}$ is4.

STEP 8

Next, let's look at the third measurement, $3.3 \times10^{-3} \mathrm{~m}$ .

STEP 9

Count the significant digits in $3.3$ .
There are two significant digits3 and3.

STEP 10

The number of significant digits in $3.3 \times10^{-3} \mathrm{~m}$ is2.

STEP 11

Finally, let's look at the fourth measurement, $40400 . \mathrm{kg}$ .

STEP 12

Count the significant digits in $40400$ .
The trailing zeros are not significant because they are not after a decimal point. The three digits before the trailing zeros (4,0, and4) are all significant.

STEP 13

The number of significant digits in $40400 . \mathrm{kg}$ is3.

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QuestionCount the significant digits in these measurements: $-8.0 \times 10^{-1} \mathrm{~kJ/mol}$ , $0.007500 \mathrm{~J}$ , $3.3 \times 10^{-3} \mathrm{~mL}$ , $40400 \mathrm{~kg}$ .

Studdy Solution

STEP 1

STEP 2

STEP 3

Count the significant digits in $-8.0$ .
There are two significant digits8 and0. The zero is significant because it is a trailing zero that comes after a decimal point.

STEP 4

The number of significant digits in $-8.0 \times10^{-1} \mathrm{~kJ} / \mathrm{mol}$ is2.

STEP 5

Next, let's look at the second measurement, $0.007500 \mathrm{~J}$ .

STEP 6

Count the significant digits in $0.007500$ .
The leading zeros are not significant. The four digits after the leading zeros (,5,0, and0) are all significant. The zeros are significant because they are trailing zeros that come after a decimal point and a non-zero digit.

STEP 7

The number of significant digits in $0.007500 \mathrm{~J}$ is4.

STEP 8

Next, let's look at the third measurement, $3.3 \times10^{-3} \mathrm{~m}$ .

STEP 9

Count the significant digits in $3.3$ .
There are two significant digits3 and3.

STEP 10

The number of significant digits in $3.3 \times10^{-3} \mathrm{~m}$ is2.

STEP 11

Finally, let's look at the fourth measurement, $40400 . \mathrm{kg}$ .

STEP 12

Count the significant digits in $40400$ .
The trailing zeros are not significant because they are not after a decimal point. The three digits before the trailing zeros (4,0, and4) are all significant.

STEP 13

The number of significant digits in $40400 . \mathrm{kg}$ is3.

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QuestionCount the significant digits in these measurements: −8.0×10−1 kJ/mol-8.0 \times 10^{-1} \mathrm{~kJ/mol}−8.0×10−1 kJ/mol, 0.007500 J0.007500 \mathrm{~J}0.007500 J, 3.3×10−3 mL3.3 \times 10^{-3} \mathrm{~mL}3.3×10−3 mL, 40400 kg40400 \mathrm{~kg}40400 kg.

Studdy Solution

STEP 1

STEP 2

STEP 3

Count the significant digits in −8.0-8.0−8.0.There are two significant digits8 and0. The zero is significant because it is a trailing zero that comes after a decimal point.

STEP 4

The number of significant digits in −8.0×10−1 kJ/mol-8.0 \times10^{-1} \mathrm{~kJ} / \mathrm{mol}−8.0×10−1 kJ/mol is2.

STEP 5

Next, let's look at the second measurement, 0.007500 J0.007500 \mathrm{~J}0.007500 J.

STEP 6

Count the significant digits in 0.0075000.0075000.007500.The leading zeros are not significant. The four digits after the leading zeros (,5,0, and0) are all significant. The zeros are significant because they are trailing zeros that come after a decimal point and a non-zero digit.

STEP 7

The number of significant digits in 0.007500 J0.007500 \mathrm{~J}0.007500 J is4.

STEP 8

Next, let's look at the third measurement, 3.3×10−3 m3.3 \times10^{-3} \mathrm{~m}3.3×10−3 m.

STEP 9

Count the significant digits in 3.33.33.3.There are two significant digits3 and3.

STEP 10

The number of significant digits in 3.3×10−3 m3.3 \times10^{-3} \mathrm{~m}3.3×10−3 m is2.

STEP 11

Finally, let's look at the fourth measurement, 40400.kg40400 . \mathrm{kg}40400.kg.

STEP 12

Count the significant digits in 404004040040400.The trailing zeros are not significant because they are not after a decimal point. The three digits before the trailing zeros (4,0, and4) are all significant.

STEP 13

The number of significant digits in 40400.kg40400 . \mathrm{kg}40400.kg is3.

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QuestionCount the significant digits in these measurements: $-8.0 \times 10^{-1} \mathrm{~kJ/mol}$ , $0.007500 \mathrm{~J}$ , $3.3 \times 10^{-3} \mathrm{~mL}$ , $40400 \mathrm{~kg}$ .

Count the significant digits in $-8.0$ .
There are two significant digits8 and0. The zero is significant because it is a trailing zero that comes after a decimal point.

The number of significant digits in $-8.0 \times10^{-1} \mathrm{~kJ} / \mathrm{mol}$ is2.

Next, let's look at the second measurement, $0.007500 \mathrm{~J}$ .

Count the significant digits in $0.007500$ .
The leading zeros are not significant. The four digits after the leading zeros (,5,0, and0) are all significant. The zeros are significant because they are trailing zeros that come after a decimal point and a non-zero digit.

The number of significant digits in $0.007500 \mathrm{~J}$ is4.

Next, let's look at the third measurement, $3.3 \times10^{-3} \mathrm{~m}$ .

Count the significant digits in $3.3$ .
There are two significant digits3 and3.

The number of significant digits in $3.3 \times10^{-3} \mathrm{~m}$ is2.

Finally, let's look at the fourth measurement, $40400 . \mathrm{kg}$ .

Count the significant digits in $40400$ .
The trailing zeros are not significant because they are not after a decimal point. The three digits before the trailing zeros (4,0, and4) are all significant.

The number of significant digits in $40400 . \mathrm{kg}$ is3.