Basic Mathematics for College Students

334 Chapter 4 Decimals

EXAMPLE (^3) Subtract 13.059 from 15.4.
StrategyWe will translate the sentence to mathematical symbols and then
perform the subtraction. As we prepare to subtract in each column, we will
compare the digit in the subtrahend (bottom number) to the digit directly above it
in the minuend (top number).
WHYIf a digit in the subtrahend is greater than the digit directly above it in the
minuend, we must borrow (regroup) to subtract in that column.
SolutionSince 13.059 is the number to be subtracted, it is the subtrahend.
To find the difference, we write the subtraction in vertical form. To help with the
column subtractions, we write two zeros to the right of 15.4 so that both numbers
have three decimal places.
Insert two zeros after the 4 so that the decimal places match.
Line up the decimal points.
Since 9 in the thousandths column of 13.05 9 is greater than 0 in the
thousandths column of 15.40 0 , we cannot immediately subtract. It is not possible to
borrow from the digit 0 in the hundredths column of 15.4 0 0. We can, however,
borrow from the digit 4 in the tenths column of 15. 4 00.
Now we complete the two-column borrowing process by borrowing from the 10 in
the hundredths column. Then we subtract, column-by-column, from the right to the
left to find the difference.
9
When 13.059 is subtracted from 15.4, the difference is 2.341.
Check:
Since the sum of the difference and the subtrahend
is the minuend, the subtraction is correct.

2.3

1

4

1

1

 13.059

15.400

Borrow 1 hundredth in the form of 10 thousandths from 10 in the

hundredths column. Add 10 to 0 in the thousandths column to

get 10 (shown in green).

15. 4

3

0

10

0

10

 13. 0 5 9

2. 3 4 1

Borrow 1 tenth in the form of 10 hundredths from 4 in the tenths column.

Add 10 to 0 in the hundredths column to get 10 (shown in blue).

15. 4

3

0

10

0

 13. 059

15. 4 00

 13. 059

15.413.059

Subtract 13.059 from 15.4

Self Check 3

Subtract 27.122 from 29.7.

Now TryProblem 31

Using Your CALCULATOR Subtracting Decimals

A giant weather balloon is made of a flexible rubberized material that has an

uninflated thickness of 0.011 inch. When the balloon is inflated with helium,

the thickness becomes 0.0018 inch. To find the change in thickness, we need to

subtract. We can use a calculator to subtract the decimals.

.011 .0018

On some calculators, the key is pressed to find the difference.

After the balloon is inflated, the rubberized material loses 0.0092 inch in

thickness.

ENTER

  0.0092