Operations with Decimals: Additional Practice (Set 2)

The divisor $0.08$ has two decimal places, so slide both points two places to the right. The divisor becomes $8$ and the dividend becomes $720$ (a trailing zero fills the second slide).

$7.2 \div 0.08 = 720 \div 8 = 90$

Dividing by a very small number gives a large quotient.

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

$5.60 - 2.34 = 3.26$

Then add the next number.

$3.26 + 1.50 = 4.76$

Multiply as whole numbers: $24 \times 25 = 600$. The factor $2.4$ has one place and $0.25$ has two, so the product has $1 + 2 = 3$ places.

$2.4 \times 0.25 = 0.600 = 0.6$

The trailing zeros can be dropped without changing the value.

Multiply as whole numbers: $24 \times 5 = 120$. The factor $0.024$ has three places and $0.5$ has one, so the product has $3 + 1 = 4$ places.

$0.024 \times 0.5 = 0.0120 = 0.012$

The trailing zero in the fourth place can be dropped.

Multiply as whole numbers: $98 \times 49 = 4802$. Each factor has one decimal place, so the product has $1 + 1 = 2$ places.

$9.8 \times 4.9 = 48.02$

The estimate $10 \times 5 = 50$ confirms the size.

Compute each. The product has two decimal places, since $4 \times 4 = 16$, and the sum lines up the tenths.

$0.4 \times 0.4 = 0.16, \qquad 0.4 + 0.4 = 0.8$

The sum $0.8$ is larger, and $0.8 - 0.16 = 0.64$, so it is larger by $0.64$.

The divisor $0.16$ has two decimal places, so slide both points two places to the right. The divisor becomes $16$ and the dividend becomes $480$ (a trailing zero fills the second slide).

$4.8 \div 0.16 = 480 \div 16 = 30$

Divide left to right. For the first division, slide both points one place so the divisor is whole.

$4.5 \div 0.9 = 45 \div 9 = 5$

Then divide that result by the next number, sliding again.

$5 \div 0.5 = 50 \div 5 = 10$

Multiply as whole numbers: $1 \times 25 = 25$. The factor $0.001$ has three places and $2.5$ has one, so the product has $3 + 1 = 4$ places.

$0.001 \times 2.5 = 0.0025$

Multiplying by $0.001$ is the same as dividing by $1000$, sliding the point three places left.

Total the two cut pieces first, lining up the points.

$1.25 + 0.80 = 2.05$

Then subtract from the board's length.

$4.50 - 2.05 = 2.45$

So $2.45$ m is left.

Multiply first, counting places: $9 \times 9 = 81$ with $1 + 1 = 2$ places.

$0.9 \times 0.9 = 0.81$

Then subtract, lining up the points.

$0.81 - 0.01 = 0.80 = 0.8$

The number of batches is the total sugar divided by the sugar per batch. Slide both points two places right so the divisor is whole.

$1.2 \div 0.15 = 120 \div 15 = 8$

So $8$ batches can be made.