Significant Figures Quiz: Can You Score Full Marks?

 All non-zero digits are significant. Zeros between digits are significant. Significant figures are the digits in a number that contribute to its precision and accuracy. In this case, each of the digits - 5, 0, and 4 - is considered significant because they provide information about the value of the number.

Remember the rules: All non-zero digits are significant. Zeros between digits are significant. Zeros in front of a number are not significant. 

The zeros before the "5" are not significant because they serve as placeholders to indicate the decimal point's position and do not contribute to the precision of the measurement. Therefore, the number 0.0504 has three significant figures.

All non-zero digits are significant. Zeros between digits are significant. Zeros in front of a number are not significant. Zeros at the end of a number that represents a measured quantity is a significant digit. Zeros to the right of a decimal point show how accurately a measurement is taken and is significant.

To determine the number of significant figures in 0.00032040:

Leading zeros (zeros before the first non-zero digit) are not significant. These only indicate the position of the decimal point.

All non-zero digits are significant because they represent measured values.

Trailing zeros after the decimal point are significant because they indicate the precision of the measurement.

In this number:

The leading zeros (0.000) are not significant.

The digits 3, 2, 0, 4, and the final zero are all significant.

Thus, the number 0.00032040 has 5 significant figures.

In the number 0.002, there is one significant figure. Leading zeros, which are zeros to the left of the first non-zero digit, are not considered significant. Therefore, only the digit 2 is counted as a significant figure in this case.

In the number "5040 toys," the zeros at the end of the number (after the non-zero digits) are not considered significant figures. They are placeholders that indicate the magnitude of the number but do not contribute to its precision.

So, in this case, there are three significant figures: "5," "0," and "4." The trailing zeros after "4" are not counted as significant.

In the mass of 504.30 grams, there are five significant figures.

Explanation:

All non-zero digits are significant.

Zeros between non-zero digits are significant.

Trailing zeros in a number containing a decimal point are significant.

So, in the number 504.30:

The digits 5, 0, 4, 3, and the final 0 are all significant.

When adding 13.4 and 2.4, both numbers have 1 decimal place. According to the rules for significant figures in addition, the result should be rounded to the least number of decimal places present in the numbers being added. Adding 13.4 and 2.4 gives 15.8. Since both original numbers have 1 decimal place, the final answer is also rounded to 1 decimal place, resulting in 15.8.

The digits 2, 1, 3, and 9 are significant because they convey meaningful information about the value.

The trailing zero (0) at the end of the number is also considered significant when it comes after a decimal point. It indicates the precision of the measurement.

So, there are five significant figures in the number 2.1390.

The digits 6, 7, 8, 0, 2, and 4 are all significant because they represent meaningful information about the value.

The trailing zeroes after the decimal point (the zeroes to the right of the decimal point) are also significant in this context. They indicate the precision of the measurement.

So, there are eight significant figures in the number 678.02400.

Significant figures indicate the precision of a measurement. In the number 1.00400, all the digits convey meaningful information. The leading '1' and the '4' are significant as non-zero digits. The zeros between them are also significant as they are captive zeros. Additionally, the trailing zeros after the decimal signify increased precision, thus contributing to the total count of significant figures.

In the number 0.004506, the leading zeros (0.00) are not significant. The significant digits are 4, 5, 0, and 6. The zero between the 5 and 6 is significant because it is between two non-zero digits. Therefore, there are a total of four significant figures in the given number.  

The sum of the numbers is:



3.01 + 2.32 + 5.1 = 10.43



When adding these numbers, you should retain the same number of decimal places as the number with the fewest decimal places, which, in this case, is "5.1." Therefore, the answer should be rounded to one decimal place:



10.43 (rounded to one decimal place)

In multiplication and division, the rule for determining the number of significant figures in the result is that it should have the same number of significant figures as the least precise number being multiplied or divided. Since 123.1 is the least precise number with 4 significant figures, the result should also have 4 significant figures.

In multiplication and division:

The result should be rounded to the same number of significant figures as the factor with the least number of significant figures.

Count the significant figures in each factor:

2.34 has 3 significant figures.

1.1 has 2 significant figures.

The unrounded result of the multiplication is:

2.34×1.1=2.574

Since the factor with the fewest significant figures (1.1) has 2 significant figures, the result must be rounded to 2 significant figures:

Rounded result: 2.6.