Operations with Decimals: Practice

Ignore the points and multiply as whole numbers: $12 \times 3 = 36$. The factor $0.12$ has two places and $0.3$ has one, so the product has $2 + 1 = 3$ places.

$0.12 \times 0.3 = 0.036$

Three places means a leading zero is needed to fill the tenths place.

First find the distance of the five laps by multiplying.

$5 \times 0.4 = 2.0$

Then add the extra distance, lining up the points.

$2.0 + 0.75 = 2.75$

The total is $2.75$ km.

Multiply as whole numbers: $15 \times 15 = 225$. Each factor has one decimal place, so the product has $1 + 1 = 2$ places.

$1.5 \times 1.5 = 2.25$

The estimate $1.5 \times 1.5$ is between $1$ and $4$, so $2.25$ is reasonable.

Subtract left to right, padding to two places and lining up the points each time.

$4.50 - 1.27 = 3.23$

Then subtract the next number.

$3.23 - 0.80 = 2.43$

Multiply as whole numbers: $5 \times 5 = 25$. Each factor has two decimal places, so the product has $2 + 2 = 4$ places.

$0.05 \times 0.05 = 0.0025$

Two leading zeros are needed to reach four decimal places.

Cost is weight times price per unit, so multiply. As whole numbers, $25 \times 18 = 450$, and the factors have one and two decimal places, for $1 + 2 = 3$ places.

$2.5 \times 1.80 = 4.500 = 4.5$

The apples cost $4.50$ dollars.

The divisor $0.04$ has two decimal places, so slide both points two places to the right. The divisor becomes $4$ and the dividend becomes $60$ (a trailing zero fills the second slide).

$0.6 \div 0.04 = 60 \div 4 = 15$

Multiply as whole numbers: $37 \times 1 = 37$. The factor $3.7$ has one place and $0.1$ has one, so the product has two places.

$3.7 \times 0.1 = 0.37$

Multiplying by $0.1$ is the same as dividing by $10$, which slides the point one place left.

The number of pieces is the total length divided by the length of one piece. Slide both points one place right so the divisor is whole.

$6.4 \div 0.8 = 64 \div 8 = 8$

There are $8$ pieces.

Pad every number to two decimal places so the columns line up: $12.50$, $0.75$, $3.40$. Then add.

$12.50 + 0.75 + 3.40 = 16.65$

Multiply as whole numbers: $104 \times 5 = 520$. The factor $1.04$ has two decimal places and $5$ has none, so the product has two places.

$1.04 \times 5 = 5.20 = 5.2$

The placeholder zero inside $1.04$ keeps the $4$ in the hundredths place.

Total cost is the per-minute cost times the number of minutes. Multiply as whole numbers ($24 \times 5 = 120$), then place two decimal places.

$24 \times 0.05 = 1.20 = 1.2$

The call costs $1.20$ dollars.