Student Resources—746

Math Skill Handbook
Math Skill Handbook
Precision and Significant
Digits
When you make a measurement, the
value you record depends on the precision
of the measuring instrument. This precision
is represented by the number of significant
digits recorded in the measurement. When
counting the number of significant digits,
all digits are counted except zeros at the end
of a number with no decimal point such as
2,050, and zeros at the beginning of a decimal
such as 0.03020. When adding or subtracting
numbers with different precision,
round the answer to the smallest number of
decimal places of any number in the sum or
difference. When multiplying or dividing,
the answer is rounded to the smallest number
of significant digits of any number
being multiplied or divided.
Example The lengths 5.28 and 5.2 are measured in
meters. Find the sum of these lengths and record your
answer using the correct number of significant digits.
Step 1 Find the sum.
5.28 m 2 digits after the decimal
5.2 m 1 digit after the decimal
10.48 m
Step 2 Round to one digit after the decimal because
the least number of digits after the decimal
of the numbers being added is 1.
The sum is 10.5 m.
Practice Problem How many significant digits are
in the measurement 7,071,301 m? How many significant
digits are in the measurement 0.003010 g?
Practice Problem Multiply 5.28 and 5.2 using the
rule for multiplying and dividing. Record the answer
using the correct number of significant digits.
788 STUDENT RESOURCES
Scientific Notation
Many times numbers used in science are
very small or very large. Because these numbers
are difficult to work with scientists use
scientific notation. To write numbers in scientific
notation, move the decimal point
until only one non-zero digit remains on
the left. Then count the number of places
you moved the decimal point and use that
number as a power of ten. For example, the
average distance from the Sun to Mars is
227,800,000,000 m. In scientific notation,
this distance is 2.278 10 11 m. Because you
moved the decimal point to the left, the
number is a positive power of ten.
The mass of an electron is about
0.000 000 000 000 000 000 000 000 000 000 911 kg.
Expressed in scientific notation, this mass is
9.11 10 31 kg. Because the decimal point
was moved to the right, the number is a
negative power of ten.
Example Earth is 149,600,000 km from the Sun.
Express this in scientific notation.
Step 1 Move the decimal point until one non-zero
digit remains on the left.
1.496 000 00
Step 2 Count the number of decimal places you have
moved. In this case, eight.
Step 3 Show that number as a power of ten, 10 8 .
The Earth is 1.496 10 8 km from the Sun.
Practice Problem How many significant digits are
in 149,600,000 km? How many significant digits are
in 1.496 10 8 km?
Practice Problem Parts used in a high performance
car must be measured to 7 10 6 m. Express this
number as a decimal.
Practice Problem A CD is spinning at 539 revolutions
per minute. Express this number in scientific
notation.