Chapter 03 of 10

Decimal Operations

How does place value guide every decimal operation?

Decimal digits represent tenths, hundredths, thousandths, and smaller place values. Accurate decimal computation depends on preserving place value, estimating first, and checking whether the final magnitude makes sense.

The big ideas

Understand these before you worry about speed.

Align place values for addition and subtraction

Line up decimal points so ones combine with ones, tenths with tenths, and so on. Add placeholder zeros when they help show matching places.

Example

\displaystyle 12.6+3.47=12.60+3.47=16.07

Count decimal places when multiplying

Multiply as if the factors were whole numbers. The product contains as many decimal places as the factors contain altogether.

Example

\displaystyle 2.4(0.35)=0.840=0.84

Make the divisor whole when dividing

Move the decimal point in both dividend and divisor by the same number of places. This creates an equivalent division problem.

Example

\displaystyle 15.75\div3.5=157.5\div35

Estimate to catch misplaced decimals

Round the numbers to nearby whole numbers before calculating. Your exact answer should be reasonably close to that estimate.

Example

\displaystyle 19.8\cdot3.1

is close to

\displaystyle 20\cdot3=60

, so

\displaystyle 6.138

cannot be correct.

Worked example

Follow the reason for each step—not just the symbols.

Problem

Evaluate $\displaystyle 15.75\div3.5$ .

Move both decimal points one place: $\displaystyle 157.5\div35$ .
$\displaystyle 35$ goes into $\displaystyle 157$ four times, using $\displaystyle 140$ and leaving $\displaystyle 17$ .
Continue through the decimal: $\displaystyle 35$ goes into $\displaystyle 175$ five times.
Check by multiplication: $\displaystyle 4.5(3.5)=15.75$ .

Answer $\displaystyle 4.5$

Try it yourself

Work on paper first. Open each answer only when you are ready to check.

Compute $\displaystyle 8.4+12.67$ .

Check answer

$\displaystyle 21.07$

Compute $\displaystyle 20-3.485$ .

Check answer

$\displaystyle 16.515$

Compute $\displaystyle 4.2(1.35)$ .

Check answer

$\displaystyle 5.67$

Compute $\displaystyle 9.36\div1.2$ .

Check answer

$\displaystyle 7.8$

Practice and tools

Use the resource that matches what you need next.

Worksheet

Decimal Operations

The big ideas

Align place values for addition and subtraction

Count decimal places when multiplying

Make the divisor whole when dividing

Estimate to catch misplaced decimals

Worked example

Evaluate $\displaystyle 15.75\div3.5$ .

Try it yourself

Practice and tools

Decimal Basics

Adding and Subtracting Decimals

Multiplying Decimals

Dividing Decimals

Money Word Problems

Align place values for addition and subtraction

Count decimal places when multiplying

Make the divisor whole when dividing

Estimate to catch misplaced decimals

Evaluate 15.75÷3.5\displaystyle 15.75\div3.515.75÷3.5.

Decimal Basics

Adding and Subtracting Decimals

Multiplying Decimals

Dividing Decimals

Money Word Problems

Evaluate $\displaystyle 15.75\div3.5$ .