Basic Mathematics for College Students

4.1 An Introduction to Decimals 323

EXAMPLE (^7) Chemistry A student
in a chemistry class uses a digital balance to
weigh a compound in grams. Round the reading
shown on the balance to the nearest thousandth
of a gram.
StrategyWe will identify the digit in the
thousandths column and the digit in the ten-
thousandths column.
WHYTo round to the nearest thousandth, the digit in the thousandths column is
the rounding digit and the digit in the ten-thousandths column is the test digit.
SolutionThe rounding digit in the thousandths column is 8. Since the test digit 7
is 5 or greater, we round up.
Rounding digit: thousandths column Add 1 to 8.
15.2387 15.2387
Test digit: 7 is 5 or greater. Drop this digit.
The reading on the balance is approximately 15.239 grams.
Self Check 7
Round 24.41658 to the nearest
ten-thousandth.
Now TryProblems 65 and 69
EXAMPLE (^8) Round each decimal to the indicated place value:
a. to the nearest tenth b.33.096 to the nearest hundredth
StrategyIn each case, we will first identify the rounding digit. Then we will
identify the test digit and determine whether it is less than 5 or greater than or
equal to 5.
WHYIf the test digit is less than 5, we round down; if it is greater than or equal
to 5, we round up.
Solution
a.Negative decimals are rounded in the same ways as positive decimals. The
rounding digit in the tenths column is 1. Since the test digit 3 is less than 5,
we round down.
Rounding digit: Keep the rounding digit:
tenths column Do not add 1.
Test digit: Drop the test digit and
3 is less than 5. all digits to its right.
Thus, rounded to the nearest tenth is
b.The rounding digit in the hundredths column is 9. Since the test digit 6 is 5 or
greater, we round up.
Add 1. Since 9  1 10, write 0
Rounding digit: in this column and carry 1 to
hundredths column. the tenths column

645.1358 645.1.

645.1358 645.1358

645.1358

Self Check 8

Round each decimal to the

indicated place value:

a. to the nearest tenth

b.9.1198 to the nearest

thousandth

Now TryProblems 73 and 77

708.522

33.096

Test digit: 6 is 5 or greater. Drop the test digit.

Thus, 33.096 rounded to the nearest hundredth is 33.10.

33.0

1

96

Caution! It would be incorrect to drop the 0 in the answer 33.10. If asked to

round to a certain place value (in this case, thousandths), that place must have

a digit, even if the digit is 0.