Working with large numbers
Some of the numbers you will work with in these investigations are quite large.
When talking about the amount of water in the ocean or the energy of an
earthquake or hurricane, you routinely use values in the billions or even trillions.
Where possible, ArcGIS has been modifi ed to make these very large and very
small numbers easier to read. For example, in the Statistics Report window shown
at left, the total area is given as million, rather than
square kilometers.
Occasionally, you will need to convert millions to billions or thousands, or vice
versa. For example, to convert the Mean value in the window at left from millions
to billions, move the decimal point three places to the left. To go from millions to
thousands, move the decimal three places to the right.
72700 thousand = 72.7 million = 0.0727 billion
Rounding
Most of these numbers are approximations, so it does not make sense to be overly
precise when you are calculating or recording them. Look at the number written
below, and the place value of each of the digits. Face it—when you are talking
about nearly billion of something, who cares about hundred-thousandths, or
even tens of millions?
Th roughout these investigations, you will be asked to round answers to a
particular value and number of decimal places, such as “Round your answer to
the nearest . million.” Rounding numbers is simple, if you follow these steps.
Examples are shown at the left.
• Look only at the numeral to the right of the place value you are rounding
to. For example, when rounding to the nearest thousand, look only at the
numeral in the hundreds place.
• If the numeral to the right is -, do not change the number you are
rounding to. If the number to the right is -, add one to the number you
are rounding to.
• Change whole numerals to the right of the place you are rounding to into
zeros, and omit all unused decimal places.
• For any number less than , include a zero to the left of the decimal point.
(Instead of . billion, write . billion.)
Rounding decimal fractions
Rounding decimals works the same way, except that you are rounding to tenths,
hundredths, thousandths, and so on. Do not add zeros to the right of the decimal
point. In other words, rounding . to the nearest tenth is ., not ..
hundred billions
ten billions
billions
hundred millions
ten millions
millions
hundred thousands
ten thousands
thousands
hundreds
tens
ones
tenths
hundredths
thousandths
ten-thousandths
hundred-thousandths
148,753,982,067.95249
Rounding examples
For example, if your number is
319,74 0,562 .8 5
To round to the nearest ten million:
• Find the ten millions digit (1).
• Look at the number to its right (9). Becau se it
is between 5 and 9, add one to the ten millions
digit to make it 2.
• Change the whole numbers to the right of
the ten millions digit to zeros and drop the
decimal point and every thing to its right. The
result is 320,000,000.
Rounding to the nearest…
…million (1,000,000) = 320,000,000
(adding 1 to 319 gives 320)
…hundred thousand (100,000) = 319,700,000
…ten thousand (10,000) = 319,740,000
…thousand (1,000) = 319,741,000
…hundred (100) = 319,740,60 0
…ten (10) = 319,740,560
…one (1) = 319,740,563
…tenth (0.1) = 319,740,562.9
To round to the nearest 0.1 million:
• Find the 0.1 millions digit (7). This is also
called the hundred thousand s digit.
• Look at the number to its right (4). Because i t
is between 0 and 4, do not add o ne to the 0.1
millions digit.
• Insert the decimal po int in the proper location.
The result is 319.7 million.
Getting started vii
Exploring the Dynamic Earth Introduction
