What Are Decimals?
- Decimals represent fractions of a whole number, such as tenths, hundredths, and thousandths.
- They are another way to express parts of a number beyond whole units, similar to fractions.
Working with Decimals
1. Adding and Subtracting Decimals?
- Align the decimal points before adding or subtracting.
- Treat decimals like whole numbers, starting from the rightmost digit.
- Examples:
- 123.5 + 234.2 = 357.7
- 72.347 64.012 = 8.335
2. Multiplying Decimals?
- Multiply as if the numbers have no decimal points.
- After calculating, adjust the decimal point in the result based on the total decimal places in the factors.
- Examples:
- 0.5 × 0.5 = 0.25 (Move decimal 2 places left).
- 1.2 × 0.25 = 0.3 (Move decimal 3 places left).
3. Dividing Decimals
- Convert the divisor into a whole number by multiplying it by 10 (or more). Do the same for the dividend.
- Perform division as with whole numbers and place the decimal point directly in the quotient.
- Example:
- 50.22 ÷ 0.2 502.2 ÷ 2 = 251.1
Tip: After solving, check if the result seems logical by estimating with rounded numbers.
Converting Between Fractions and Decimals
1. Decimals to Fractions
- Write the decimal over 1, then multiply numerator and denominator by 10 until there are no decimals.
- Simplify the fraction if possible.
- Examples:
- 0.25 25/100 1/4
- 1.25 125/100 5/4 1 1/4
2. Fractions to Decimals
- Treat the fraction as a division: numerator ÷ denominator.
- Add zeros after the decimal point if needed to complete the calculation.
- Examples:
- 1/2 = 0.5
- 4/25 = 4 ÷ 25 = 0.16
Key Points to Remember
- Decimal places matter: Always align and track the decimal position in calculations.
- Check results: If the answer looks wrong, recheck the position of the decimal point.
- Decimals are fractions: They follow the same rules but require attention to detail.
With practice, decimals become as easy to manage as whole numbers.