Question 1

Trailing zeros before a decimal point but after a non-zero number are considered significant figures.

Accepted Answer

Trailing zeros after a non-zero number are considered significant figures. This is because they indicate the precision of the measurement or calculation.

Question 2

The decimal number 0.0210 expressed in scientific notation is 2.10 × 10^-2.

Accepted Answer

To express a decimal number in scientific notation, we move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. The number of places we moved the decimal point becomes the exponent of 10. So, 0.0210 can be written as 2.10 × 10^-2. The notation given in the question matches this format, hence the answer is A.

Question 3

Zeros located between two numbers are not significant.

Accepted Answer

Zeros located between two numbers are considered significant because they indicate the precision of the measurement.

Question 4

Numbers are usually written so that the uncertainty is in the last reported digit.

Accepted Answer

This is a common convention in scientific measurements and calculations. The uncertain digit is often written as a decimal point followed by one or more digits that represent the uncertainty or error in the measurement. For example, a measurement of 3.50 cm might have an uncertainty of +/- 0.01 cm, and would be written as 3.50 +/- 0.01 cm. In this case, the uncertainty is in the last reported digit (the digit after the decimal point).

Question 5

Exact numbers have an unlimited number of significant figures.

Accepted Answer

Exact numbers are considered to have an infinite number of significant figures because they are not obtained through measurement or calculation. Examples of exact numbers include counting objects, exact values of constants, and areas of geometric shapes with defined dimensions.

Question 6

In multiplication and division calculations,the answer will have the same number of decimal places as the number carrying the fewest decimal places.

Accepted Answer

In multiplication, the answer will have the total number of decimal places as the sum of decimal places in the factors. In division, the answer can have a maximum number of decimal places equal to the number of decimal places in the dividend.

Question 7

The mass of an object,4.55 ×  g,expressed in decimal notation is 0.000455 g.

Accepted Answer

The answer of The mass of an object,4.55 × ...

Question 8

If you count 7 pennies,you can only report one significant figure in that measurement.

Accepted Answer

Counting exact numbers, like 7 pennies, gives a result that is considered to have an infinite number of significant figures because it is an exact count.

Question 9

In multiplication or division calculations,the answer will have the same number of decimal places as the number carrying the most decimal places.

Accepted Answer

In multiplication or division calculations, the answer will have the same number of significant figures as the number carrying the least number of significant figures. The number of decimal places in the answer depends on the specific calculation and cannot be determined by the number of decimal places in the original numbers alone.

Question 10

The number 7.20 × 10³ contains three significant figures.

Accepted Answer

The three significant figures in the number are 7.20, which means the digits 1, 3, and 0 are not significant. The 10³ part is simply scientific notation indicating the exponent of the power of 10 by which the number is multiplied.

Question 11

Scientific numbers are reported so that every digit is certain except the last,which is estimated.

Accepted Answer

Scientific numbers are reported with a certain number of significant digits, in which every digit except the last one is considered certain. The uncertain digit is estimated based on the precision of the measuring instrument used to obtain the measurement. Therefore, the statement is true.

Question 12

The number 0.010100 has five significant figures.

Accepted Answer

The non-zero digits 1 and 5 are significant, and the zeros between them are also significant in this case because they come after the decimal point. Therefore, the number 0.010100 has a total of five significant figures.

Question 13

When the temperature of an object is reported as 23.7°C,the actual temperature can be assumed to be between 23.6°C and 23.8°C.

Accepted Answer

The given temperature of 23.7°C has one decimal point, indicating that the measurement has been made with a thermometer that is accurate up to one decimal point. Generally, such thermometers are calibrated to give a reading with an uncertainty of ±0.1°C. Therefore, the actual temperature can be assumed to be between 23.6°C and 23.8°C. Hence, the statement is true.

Question 14

The decimal number 0.0000010 expressed in scientific notation is 1.0 × 10⁶.

Accepted Answer

The correct scientific notation for 0.0000010 is 1.0 × 10^-6. The exponent should be negative, not positive, and the positions of the symbols for the sign, coefficient, and exponent are not accurate in the given expression.

Question 15

Trailing zeros at the end of a number,but before an implied decimal point,are ambiguous.

Accepted Answer

Trailing zeros at the end of a number, without a decimal point, can be interpreted as significant or insignificant. However, when there is an implied decimal point, the trailing zeros become significant and should be included. Therefore, the presence or absence of trailing zeros without a decimal point can be ambiguous.

Question 16

When the number 2.35 is rounded to contain 2 significant figures it becomes 2.4.

Accepted Answer

When rounding to 2 significant figures, the rule is to look at the digit in the third place. If it is 5 or greater, round up the digit in the second place. In this case, the digit in the third place is 5, so the digit in the second place (3) rounds up to 4. Therefore, 2.35 rounded to 2 significant figures is 2.4.

Question 17

When the number 65.59 is rounded to contain 2 significant figures,it becomes 66.0.

Accepted Answer

When rounding the number 65.59 to two significant figures, it becomes 66, not 66.0, because the second significant figure is the 6 in the tens place, and the 5 in the units place rounds up.

Question 18

The number 4,450,000.0 has 3 significant figures.

Accepted Answer

The number 4,450,000.0 has 7 significant figures because the decimal point indicates that all zeros are significant.

Question 19

Zeros located after a number and after a decimal point are significant.

Accepted Answer

Zeros located after a number and after a decimal point are significant. For example, 4500 has 2 significant digits, while 4500. has 4 significant digits.

Question 20

In addition or subtraction,the result carries the same number of decimal places as the quantity carrying the fewest decimal places.

Accepted Answer

This is known as the rule of significant figures or decimal places in math. It ensures that the result is not reported with more precision than the least precise input value.

Quiz 2: Measurement and Problem Solving