Working with Precision: Decimal Operations
Decimal operations β adding, subtracting, multiplying, and dividing numbers with decimal points β are the backbone of everyday calculations involving money, measurements, and data. Aligning decimal points, counting decimal places, and moving decimals are the key techniques that keep answers accurate.
Components of Decimal Operations
This section covers the four operations with decimals:
- Adding Decimals: Line up the decimal points, add column by column from right to left, and carry as needed.
- Subtracting Decimals: Line up the decimal points, subtract column by column, and borrow when necessary.
- Multiplying Decimals: Multiply as if the numbers were whole numbers, then place the decimal point by counting total decimal places in the factors.
- Dividing Decimals: Move the decimal in the divisor to make it a whole number, shift the dividend the same number of places, then divide normally.
Examples of Decimal Operations
Adding Decimals Examples
- Add 3.25 + 1.7: Align the decimal points (write 1.7 as 1.70), then 3.25 + 1.70 = 4.95.
- Add 0.006 + 0.14: Align as 0.006 + 0.140 = 0.146.
- A shopping cart has items costing $4.59 and $12.35. Add 4.59 + 12.35 = $16.94 total.
Subtracting Decimals Examples
- Subtract 5.4 - 2.78: Write 5.4 as 5.40, then 5.40 - 2.78 = 2.62.
- Subtract 10 - 3.625: Write 10 as 10.000, then 10.000 - 3.625 = 6.375.
- A runner's previous time was 58.3 seconds and the new time is 55.87 seconds. The improvement is 58.30 - 55.87 = 2.43 seconds.
Multiplying Decimals Examples
- Multiply 2.5 Γ 0.4: Multiply 25 Γ 4 = 100, then place the decimal (1 + 1 = 2 total decimal places) to get 1.00 = 1.
- Multiply 3.12 Γ 2.5: Multiply 312 Γ 25 = 7,800, then place the decimal (2 + 1 = 3 places) to get 7.800 = 7.8.
- Gasoline costs $3.45 per gallon and you buy 8.2 gallons. Multiply 3.45 Γ 8.2 = 28.29 dollars.
Dividing Decimals Examples
- Divide 7.5 Γ· 2.5: Move the decimal one place in both to get 75 Γ· 25 = 3.
- Divide 0.456 Γ· 0.08: Move two places in both to get 45.6 Γ· 8 = 5.7.
- A 2.4-kilogram bag of rice is split into 0.3-kilogram servings. Divide 2.4 Γ· 0.3 = 8 servings.