Working with Decimals

Learn to add, subtract, multiply, and divide decimals

Understanding Decimals

Decimals are another way to represent parts of a whole.

Place value: $3.475$

Rule: Line up the decimal points!

&3.45 \\ + &2.7 \\ \hline &6.15 \end{align}$$ ## Multiplying Decimals Steps: 1. Multiply as if they're whole numbers 2. Count total decimal places in both numbers 3. Put that many decimal places in the answer **Example:** $2.5 \times 0.3 = 0.75$ (2 decimal places total) ## Dividing Decimals Steps: 1. Move the decimal in the divisor to make it a whole number 2. Move the decimal in the dividend the same number of places 3. Divide normally 4. Place the decimal point in the quotient ## Converting Between Fractions and Decimals - **Fraction to decimal:** Divide numerator by denominator - **Decimal to fraction:** Use place value ($0.75 = \frac{75}{100} = \frac{3}{4}$)

Calculate: $5.6 + 3.84$

💡 Show Solution

Solution:

Line up the decimal points:

&5.60 \\ + &3.84 \\ \hline &9.44 \end{align}$$ **Answer:** $9.44$

Calculate: $3.2 \times 1.5$

💡 Show Solution

Solution:

Multiply as whole numbers: $32 \times 15 = 480$

Count decimal places (1 + 1 = 2 places): $480 \rightarrow 4.80 = 4.8$

Answer: $4.8$

A rope is 15.6 meters long. It is cut into 4 equal pieces. How long is each piece?

💡 Show Solution

Solution:

Divide: $15.6 \div 4$

&\phantom{0}3.9 \\ 4 &\overline{)15.6} \\ &\underline{12\phantom{.0}} \\ &\phantom{0}3.6 \\ &\phantom{0}\underline{3.6} \\ &\phantom{00}0 \end{align}$$ **Answer:** Each piece is $3.9$ meters long

Review key concepts with our flashcard system

Explore other calculus topics