Name: __key___
Hour: __________
PROBLEM TO STUDY: How do you read and record measurements if the measured
object is smaller than the scale on the ruler?
Action
Obtain a meter stick
that has no divisions
between 0 and
100cm.
Purposeful Change
Independent Var.
Type of ruler
(sensitivity)
Response to Change
Dependent Variable
Length, width, and
depth measurements
in centimeters.
Remains the Same
Constant Variables
 Alignment of the
starting end of
ruler.
 Keeping ruler
perpendicular
 Finding the place
to measure 2nd
edge.
Length of shelf
Width of Shelf
Depth of Shelf
Measure the length,
width, and thickness
of the shelf board
provided.
Record these values
on the data table.
DATA:
Smallest Division on
Ruler
1 meter
100 cm
80cm
30cm
To small to measure
ANALYSIS:
1.
Where there any digits in the length and width that were not estimated? The
zeros
2.
How confident do you feel about these measurements? Not very confident. The
only digits are estimated.
3.
Did you find the Depth measurement harder to estimate reliably that the other two
measurements? Why? If you are estimating to the 10 cm place or the tenth of a
meter then the proper estimate would either be 10cm or 0cm. the thickness is
actually closer to the zero estimate that it is to the 10 cm estimate. But you are
ony allowed to estimate 1/10 th the way between the smallest division which is to
the closest 10 cm.
PROBLEM TO STUDY: How will the values of a measurement and the number of
digits in a measurement change when an object is measured with a ruler with 10cm
divisions.
Action
Obtain a meter stick
that has 10 cm
divisions.
Purposeful Change
Independent Var.
Type of ruler
(sensitivity)
Response to Change
Dependent Variable
Length, width, and
depth measurements
in centimeters.
Measure the length,
width, and thickness
of the shelf board
provided.
Remains the Same
Constant Variables
 Alignment of the
starting end of
ruler.
 Keeping ruler
perpendicular
Record these values
on the data table.
Hypothesis: If a ruler with smaller divisions is used, then the measurement will have
(more, less, or the same number) reliable digits.
DATA:
Smallest Division on
Ruler
1 meter
100 cm
1 decimeter 10 cm
Length of shelf
Width of Shelf
80cm
79cm
30cm
29cm
Depth of Shelf
To small to measure
2cm
ANALYSIS:
4.
Were there any digits in the new measurements that could be determined for
certain without estimating? Which digits and in which measurements? The “7”
in the length and the “2” in the width. There are no certain digits in the depth.
5.
State how to determine the last digit of a measurement from the smallest division
on the ruler. The smallest division was each 10 centimeters. Therefore you need
to estimate to 1/10th of the smallest division which means to estimate to the
nearest 1 cm.
6.
Significant digits are all the certain digits of a measurement plus one estimated
digit. How many significant digits do the first set of measurements contain?
How many do the last set of measurements have?
Smallest Division on Ruler
1 meter
100 cm
1 decimeter 10 cm
Length of shelf
1
2
Width of Shelf
1
2
Depth of Shelf
none
1
PROBLEM TO STUDY: How will the values of a measurement and the number of digits
in a measurement change when an object is measured with a ruler with 0.1cm divisions?
Action
Obtain a meter stick
that has 0.1 cm
divisions.
Purposeful Change
Independent Var.
Type of ruler
(sensitivity)
Response to Change
Dependent Variable
Length, width, and
depth measurements
in centimeters.
Measure the length,
width, and thickness
of the shelf board
provided.
Remains the Same
Constant Variables
 Alignment of the
starting end of
ruler.
 Keeping ruler
perpendicular
 Finding the place
to measure 2nd
edge.
Record these values
on the data table.
Hypothesis: If a ruler with 0.1cm divisions is used, then the measurement will have
(more, less, or the same number) reliable digits.
DATA:
Smallest Division on
Ruler
1 meter
100 cm
1 decimeter 10 cm
1 millimeter
0.1 cm
Length of shelf
Width of Shelf
Depth of Shelf
80cm
79cm
30cm
29cm
To small to measrue
2cm
79.11cm
28.93cm
2.52cm
ANALYSIS:
7.
State how to determine the last digit of a measurement from the smallest division
on the ruler. The smallest division is 0.1 cm. Proper measurement practices are
to estimate to 1/10th of the smallest division which is to the nearest 0.01cm.
8.
How do you determine the number of significant digits in a measurement? Count
all the digits you know for certain (all digits that represent a division on the
measuring instrument) and estimate one more digit.
9.
How many significant digits are in each of the last measurements?
Smallest Division on
Length of shelf
Width of Shelf
Depth of Shelf
Ruler
1 millimeter 0.1 cm
4
4
3
Record the Following Measurements in centimeters.
11.
124.5 to 124.8 cm
12.
125.0 cm ± 0.1 cm
13.
120.0 cm ± 0.1 cm
How many significant digits (figures) are in each of the following measurements?
14.
2305 m 4
15.
200 cm 1
16.
200. Cm 3
17.
200.00 cm 5
18.
2.0 X 102 cm 2
19.
0.006060g 4
20.
0.0230L 3
21.
Write a general rule that states how to determine the number of significant digits
(figures) in a measurement when being read by a different person (one who did not take
the measurement).



When reading left to right, the first significant digit is the first digit that is not
zero.
Count all digits (zeros and non-zeros) until you reach the last digit that is not zero.
If there are zeros following the last non-zero digit (to the far right of the last nonzero digit) they are included as significant only if a decimal point is visible in the
number and not just an understood decimal.