Math / Numbers & Operations

Question6. Determine the number of significant digits in each of the following. a) 54.05 b) 0.0045 c) 0.23040 d) $34500 \mid$

Studdy Solution

STEP 1

1. Significant digits are the digits in a number that contribute to its precision.
2. All non-zero digits are considered significant.
3. Any zeros between significant digits are also significant.
4. Leading zeros are not significant.
5. Trailing zeros in a decimal number are significant.
6. Trailing zeros in a whole number without a decimal point may or may not be significant, depending on context.

STEP 2

1. Analyze each number to identify significant digits.
2. Count the significant digits for each number.

STEP 3

Examine the number $54.05$ : - All non-zero digits are significant: $5, 4, 0, 5$ . - The zero is between significant digits, so it is also significant.

STEP 4

Count the significant digits in $54.05$ : - There are $4$ significant digits.

STEP 5

Examine the number $0.0045$ : - Leading zeros are not significant. - The digits $4$ and $5$ are non-zero and significant.

STEP 6

Count the significant digits in $0.0045$ : - There are $2$ significant digits.

STEP 7

Examine the number $0.23040$ : - Leading zeros are not significant. - The digits $2, 3, 0, 4$ are significant. - The trailing zero is significant because it is in a decimal number.

STEP 8

Count the significant digits in $0.23040$ : - There are $5$ significant digits.

STEP 9

Examine the number $34500 \mid$ : - The digits $3, 4, 5$ are significant. - The trailing zeros may or may not be significant, depending on context. Without additional information, it is common to assume they are not significant.

STEP 10

Count the significant digits in $34500 \mid$ : - Assuming the trailing zeros are not significant, there are $3$ significant digits.
The number of significant digits for each part is: a) $4$ b) $2$ c) $5$ d) $3$

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Question6. Determine the number of significant digits in each of the following. a) 54.05 b) 0.0045 c) 0.23040 d) $34500 \mid$

Studdy Solution

STEP 1

STEP 2

1. Analyze each number to identify significant digits.
2. Count the significant digits for each number.

STEP 3

Examine the number $54.05$ : - All non-zero digits are significant: $5, 4, 0, 5$ . - The zero is between significant digits, so it is also significant.

STEP 4

Count the significant digits in $54.05$ : - There are $4$ significant digits.

STEP 5

Examine the number $0.0045$ : - Leading zeros are not significant. - The digits $4$ and $5$ are non-zero and significant.

STEP 6

Count the significant digits in $0.0045$ : - There are $2$ significant digits.

STEP 7

Examine the number $0.23040$ : - Leading zeros are not significant. - The digits $2, 3, 0, 4$ are significant. - The trailing zero is significant because it is in a decimal number.

STEP 8

Count the significant digits in $0.23040$ : - There are $5$ significant digits.

STEP 9

Examine the number $34500 \mid$ : - The digits $3, 4, 5$ are significant. - The trailing zeros may or may not be significant, depending on context. Without additional information, it is common to assume they are not significant.

STEP 10

Count the significant digits in $34500 \mid$ : - Assuming the trailing zeros are not significant, there are $3$ significant digits.
The number of significant digits for each part is: a) $4$ b) $2$ c) $5$ d) $3$

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Question6. Determine the number of significant digits in each of the following. a) 54.05 b) 0.0045 c) 0.23040 d) 34500∣34500 \mid34500∣

Studdy Solution

STEP 1

STEP 2

1. Analyze each number to identify significant digits.2. Count the significant digits for each number.

STEP 3

Examine the number 54.05 54.05 54.05: - All non-zero digits are significant: 5,4,0,5 5, 4, 0, 5 5,4,0,5. - The zero is between significant digits, so it is also significant.

STEP 4

Count the significant digits in 54.05 54.05 54.05: - There are 4 4 4 significant digits.

STEP 5

Examine the number 0.0045 0.0045 0.0045: - Leading zeros are not significant. - The digits 4 4 4 and 5 5 5 are non-zero and significant.

STEP 6

Count the significant digits in 0.0045 0.0045 0.0045: - There are 2 2 2 significant digits.

STEP 7

Examine the number 0.23040 0.23040 0.23040: - Leading zeros are not significant. - The digits 2,3,0,4 2, 3, 0, 4 2,3,0,4 are significant. - The trailing zero is significant because it is in a decimal number.

STEP 8

Count the significant digits in 0.23040 0.23040 0.23040: - There are 5 5 5 significant digits.

STEP 9

Examine the number 34500∣ 34500 \mid 34500∣: - The digits 3,4,5 3, 4, 5 3,4,5 are significant. - The trailing zeros may or may not be significant, depending on context. Without additional information, it is common to assume they are not significant.

STEP 10

Count the significant digits in 34500∣ 34500 \mid 34500∣: - Assuming the trailing zeros are not significant, there are 3 3 3 significant digits. The number of significant digits for each part is: a) 4 4 4 b) 2 2 2 c) 5 5 5 d) 3 3 3

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Question6. Determine the number of significant digits in each of the following. a) 54.05 b) 0.0045 c) 0.23040 d) $34500 \mid$

1. Analyze each number to identify significant digits.
2. Count the significant digits for each number.

Examine the number $54.05$ : - All non-zero digits are significant: $5, 4, 0, 5$ . - The zero is between significant digits, so it is also significant.

Count the significant digits in $54.05$ : - There are $4$ significant digits.

Examine the number $0.0045$ : - Leading zeros are not significant. - The digits $4$ and $5$ are non-zero and significant.

Count the significant digits in $0.0045$ : - There are $2$ significant digits.

Examine the number $0.23040$ : - Leading zeros are not significant. - The digits $2, 3, 0, 4$ are significant. - The trailing zero is significant because it is in a decimal number.

Count the significant digits in $0.23040$ : - There are $5$ significant digits.

Examine the number $34500 \mid$ : - The digits $3, 4, 5$ are significant. - The trailing zeros may or may not be significant, depending on context. Without additional information, it is common to assume they are not significant.

Count the significant digits in $34500 \mid$ : - Assuming the trailing zeros are not significant, there are $3$ significant digits.
The number of significant digits for each part is: a) $4$ b) $2$ c) $5$ d) $3$