CECmath.42


TITLE:    SIGNIFICANT FIGURES

AUTHOR:   Michael T. Schultz, Cambridge high School,
          Cambridge, Idaho

GRADE LEVEL/SUBJECT:  Appropriate for grades 9-12.

OVERVIEW:  Students traditionally have a very difficult time
understanding which digits are significant, especially
zeroes, in a number that represents something that has been
measured.  This activity was designed so that students will
explore and truly understand which digits are significant
when dealing with numbers that represent measured values.

OBJECTIVE(s):  Students will be able to:
1.   use a measuring instrument to the limit of its
     precision.
2.   determine which digit in a measured value is the
     most certain.
3.   determine which digit in a measured value is the
     first uncertain value.
4.   understand when zeroes are significant when
     determining the number of significant digits in a
     measured number.

RESOURCES/MATERIALS:
*** Teacher Materials ***(For each pair of students):
1 blue paper ruler described below
1 red paper ruler described below
1 yellow paper ruler described below
several strips of green paper of different lengths (make
     sure some of them come out to where zeroes will show
     up in the measurements)

*** Student Materials ***  (For each pair of students):
1 writing utensil,
1 piece of paper to record results.

ACTIVITIES:

1.   Using a blue paper ruler with marks of 0 on one end and
     10 on the other end, measure several smaller pieces of
     green paper strips recording the results.
2.   Using a red paper ruler the same length as the blue one
     up above but divided into 10 equal spacings with only
     marks of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 on it,
     measure the same green paper strips you measured in
     activity 1 and record your results.
3.   Using a yellow paper ruler the same length as the red
     one up above but with 10 additional marks between each
     mark found on the red ruler, measure the same green
     paper strips you measured in activity 1 above and
     record your results.
4.   Have students analyze the results and discuss which
     digit in a measurement is the most certain.
5.   Have students analyze the results and discuss which
     digit in a measurement is the first uncertain digit.
6.   Discuss with students those measurements with zeroes in
     them to get students to understand when those zeroes
     are significant and when they are not.

TYING IT ALL TOGETHER:  Many students have a very difficult
time understanding significant digits and why they are
important in future calculations just by memorizing rules.
Using carefully selected green paper strips for students to
measure, the students themselves can come up with the rules
for which digits are significant and their importance in
future calculations.  This activity can be referred to when
discussing significant figures in calculations.