Question

1. if you removed a significant zero from the end of a number, would the numeric value of the number change?

placeholder zeros are very important - they help put the decimal point in the correct spot. however, they are not significant when it comes to the certainty of a measurement. in other words, placeholder zeros cannot be a certain or estimated digit in a measurement. they may show up in calculations, however. for example, if you convert 29.3 m to 29,300 mm, the zeros that you add to the measurement were not read from the measuring instrument.

1. determine if the zeros in the measurements below are significant or not. if a zero is significant, underline it.

a. 650 m b. 42.0 s c. 7000 l
d. 3.000 kg e. 0.008 ml f. 0.00560 cm

1. here are five rules for determining which digits in a measurement are significant. match each rule to a set of examples in the table below. the significant digits in each example are underlined.

rule 1: all non - zero numbers are significant.
rule 2: sandwiched zeros (those that occur between two significant digits) are significant.

Explanation:

Step1: Analyze question 15

A significant zero at the end of a number is part of the measurement's certainty. Removing it changes the numeric value. For example, 5.0 has a different value than 5.

Step2: Analyze question 16 - a

In 650 m, the zero is a placeholder (no decimal point), so it's not significant.

Step3: Analyze question 16 - b

In 42.0 s, the zero after the decimal is significant as it indicates precision. So we underline it: 42.\underline{0} s

Step4: Analyze question 16 - c

In 7000 L, the zeros are placeholders (no decimal point), so they are not significant.

Step5: Analyze question 16 - d

In 3.000 kg, all zeros after the decimal are significant. So we underline them: 3.\underline{000} kg

Step6: Analyze question 16 - e

In 0.008 mL, the zeros before the 8 are placeholders, so they are not significant.

Step7: Analyze question 16 - f

In 0.00560 cm, the zero before the 5 is a placeholder, but the zero after 6 is significant as it indicates precision. So we underline it: 0.0056\underline{0} cm

Answer:

1. Yes, the numeric value would change.
2. a. 650 m (no underlined zero)

b. 42.\underline{0} s
c. 7000 L (no underlined zero)
d. 3.\underline{000} kg
e. 0.008 mL (no underlined zero)
f. 0.0056\underline{0} cm