Significant Zeros Worksheet Answers
Significant Zeros Worksheet Answers
Significant Zeros Worksheet Answers
Significant Zeros
Which zeros are significant in a measurement, and which are simply important?
Why?
When working with measurements, it is important to know which digits in the measurement are signifi-
cant and which are not. Non-zero digits are always significant. However, zeros can be tricky; some are
significant, others are not. This activity will help you learn the rules for determining whether a zero digit
is significant or not.
Significant Zeros 1
3. Rock C is placed on the Econo-Balance. The balance reads 200 g.
a. Does rock C have a mass larger, smaller or the same as sample A, or is it impossible to tell?
Explain your reasoning.
Rock C has a larger mass than Rock A, because 200g is greater than 100g.
b. Does rock C have a mass larger, smaller or the same as rock B, or is it impossible to tell?
Explain your reasoning.
It is impossible to tell because the Econo-Balance only measures in increments of
100. Since the measurement is rounded, the masses could be different.
4. The mass of rock C is then measured using the other three balances. The results are shown
below.
Econo-Balance 200 g Balance Pro 177 g
Good Balance 180 g Exacto-Balance 177.0 g
a. Based on this additional information, does rock C have a mass larger, smaller or the same as
rock B, or is it impossible to tell? Explain your reasoning.
It is impossible to tell. Even though, per the Exacto-Balance, Rock B has a mass of 177.1g,
the .1 at the end is estimated. Therefore, Rock C and Rock B could have the same mass,
but they also might not.
b. Explain why the zero in the Exacto-Balance reading provides important information about
the mass of rock C, but the zero in the Good Balance reading does not.
The zero in the Exacto-Balance reading is important because, being the last digit, it is
estimated. However, the zero in the Good Balance reading is neither estimated nor certain.
It is simply there because it has to be in order for 180 to be read as 180.
0g 0.02 g 0.016 g
0g 0.02 g 0.020 g
8. The mass reading of pebble B from the Super Balance is 0.020 g. This value is very close, but dif-
ferent than, the mass reading for pebble A on that same balance. Determine which of the three
zeros in the mass reading for pebble B is the most significant in terms of determining whether
pebble B has a different mass than pebble A, and circle the zero below.
Mass pebble B = 0.020 g
Significant Zeros 3
Model 3 – Types of Zeros
200 g
0.02 g
180 g
0.016 g
140 g 100 g
Placeholder Zeros }
0.020 g 177.0 g 143.0 g Significant Zeros
(underlined)
9. Model 3 shows several of the measurements from Model 1 and Model 2. The zeros in those
measurements are categorized into two types. List the two types.
Placeholder zeros and significant zeros.
10. Consider the term “placeholder” as it is used in the English language. Discuss two examples of
this term in your group, and summarize them here.
A placeholder can be a bookmark, which is used so you don’t lose your place while reading.
In legal terms, a placeholder can mean someone who is authorized to act for another person.
12. If you removed a placeholder zero from a number, would the numeric value of the number
change?
Yes.
13. Describe the location of significant zeros in a number relative to the decimal point.
They are after the decimal point and at the end of the number.
14. If you removed a significant zero from the end of a number, would the numeric value of the
number change?
No.
Read This!
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.
17. In the measurements below, the significant digits are underlined. Determine the rule(s) that were
used to decide which digits were significant, and which were not significant.
a. 0.420 g b. 2100 g c. 51.0 m
Rules 1 and 4 Rules 1 and 3 Rules 1 and 4
Significant Zeros 5
Extension Questions
Model 4 – Scientific Notation (Significant digits are underlined.)
A. 3 × 104 m = 30,000 m B. 7 × 10–3 kg = 0.007 kg
3.00 × 104 m = 30,000 m 7.00 × 10–3 kg = 0.00700 kg
19. The measurements in Model 4 are written in both scientific notation and expanded notation.
Copy one example of each below.
Scientific notation Expanded notation
3 x 10^4m 30,000m
21. Look at all of the measurements in Model 4. When a number in scientific notation is changed
to expanded notation, are any of the added zeros significant? Give two examples to support your
answer.
No. 3.00 x 10^4m = 30,000. 4.10 x 10^4m = 41,000.
22. When a number in scientific notation contains a significant zero, is that zero also significant in
the expanded notation? Give two examples to support your answer.
Yes. 3.00 x 10^4m = 30,000. 4.10 x 10^4m = 41,000.
23. Write each of the measurements below in expanded notation and underline the significant digits.
a. 5.0780 × 106 g = 5,078,000 g b. 4.800 × 10–4 L = .0004800 L
c. 0.7200 × 104 mm = 7,200 mm d. 3700 × 10–3 cm = 3.7 cm