Operations with Decimals: Practice

Pad $1.3$ to two decimal places so the columns line up: $1.3 = 1.30$. Then add with the points aligned.

$2.45 + 1.30 = 3.75$

The hundredths give $5 + 0 = 5$, the tenths give $4 + 3 = 7$, and the ones give $2 + 1 = 3$.

Ignore the points and multiply as whole numbers: $4 \times 2 = 8$. Each factor has one decimal place, so the product has $1 + 1 = 2$ places.

$0.4 \times 0.2 = 0.08$

Multiplying two numbers below one gives something smaller, so a leading zero is needed.

Multiply as whole numbers: $12 \times 3 = 36$. The factors have one place each, so the product has $1 + 1 = 2$ places.

$1.2 \times 0.3 = 0.36$

Dividing by $100$ slides the decimal point two places to the left.

$27.6 \div 100 = 0.276$

A placeholder zero fills the tenths place after the point.

The divisor $0.3$ has one decimal place, so slide both points one place to the right. The divisor becomes $3$ and the dividend becomes $15$.

$1.5 \div 0.3 = 15 \div 3 = 5$

Moving both points the same amount leaves the quotient unchanged.

Pad $0.8$ to two decimal places so the columns line up: $0.8 = 0.80$. Then add with the points aligned.

$0.07 + 0.80 = 0.87$

Lining up the points keeps tenths over tenths, so the $8$ stays in the tenths place.

Multiply as whole numbers: $6 \times 5 = 30$. Each factor has one place, so the product has two places.

$0.6 \times 0.5 = 0.30 = 0.3$

The trailing zero can be dropped without changing the value.

Multiply as whole numbers: $6 \times 7 = 42$. Each factor has one place, so the product has two places.

$0.6 \times 0.7 = 0.42$

Multiply as whole numbers: $25 \times 4 = 100$. Each factor has one decimal place, so the product has two places.

$2.5 \times 0.4 = 1.00 = 1$

Pad every number to two decimal places so the columns line up: $1.60$, $2.45$, $0.50$. Then add.

$1.60 + 2.45 + 0.50 = 4.55$

The divisor $0.4$ has one decimal place, so slide both points one place to the right. The divisor becomes $4$ and the dividend becomes $36$.

$3.6 \div 0.4 = 36 \div 4 = 9$

Multiplying by $1000$ slides the decimal point three places to the right.

$0.125 \times 1000 = 125$

Three zeros means three places, which clears the point entirely.