Matemática Elementar

Problema 1

Write each number in the requested form.

(a) Write $4.072$ in expanded form using fractions.

(b) Write "nine and three hundred fifty-six thousandths" in standard form.

Problemas

1. Write each number in the requested form.

(a) Write $4.072$ in expanded form using fractions.

(b) Write "nine and three hundred fifty-six thousandths" in standard form.

2. Round each decimal to the place indicated.

(a) Round $6.847$ to the nearest tenth.

(b) Round $12.395$ to the nearest hundredth.

3. A scientist measures three samples of a chemical. The masses are $2.75$ grams, $3.084$ grams, and $1.6$ grams.

(a) What is the total mass of all three samples? Show your work, aligning decimal points.

(b) How much heavier is the second sample than the third sample?

4. A ribbon costs $\$ 1.35 $per meter. A craft project needs$ 4$ meters of ribbon.

(a) Estimate the total cost by rounding $\$ 1.35$ to the nearest dollar, then multiplying.

(b) Find the exact cost by computing $1.35 \times 4$ . Show your work.

5. A water tank holds $9.6$ liters of water. The water is poured equally into $4$ containers.

(a) How many liters does each container get? Show your division work.

(b) If each container already had $0.85$ liters of water in it, how much water is in each container now?

Gabarito — Decimal Operations

1. (a) $4.072$ in expanded form:

$4 \times 1 + 0 \times \frac{1}{10} + 7 \times \frac{1}{100} + 2 \times \frac{1}{1{,}000}$

Which simplifies to $4 + \frac{7}{100} + \frac{2}{1{,}000}$ .

(b) Nine and three hundred fifty-six thousandths:

$9.356$

(c) Compare $3.405$ and $3.450$ :

Ones: both are $3$ .
Tenths: $4 = 4$ .
Hundredths: $0 < 5$ .

$3.405 < 3.450$

2. (a) $6.847$ rounded to the nearest tenth:

Look at the hundredths digit: $4 < 5$ , so round down.

$6.847 \approx 6.8$

(b) $12.395$ rounded to the nearest hundredth:

Look at the thousandths digit: $5 \geq 5$ , so round up.

$12.395 \approx 12.40$

(c) $0.0552$ rounded to the nearest hundredth:

Look at the thousandths digit: $5 \geq 5$ , so round up.

$0.0552 \approx 0.06$

3. (a) Align the decimal points (fill with zeros as needed):

$\begin{array}{r} 2.750 \\ 3.084 \\ +\; 1.600 \\ \hline 7.434 \end{array}$

Thousandths: $0 + 4 + 0 = 4$
Hundredths: $5 + 8 + 0 = 13$ (write $3$ , carry $1$ )
Tenths: $7 + 0 + 6 + 1 = 14$ (write $4$ , carry $1$ )
Ones: $2 + 3 + 1 + 1 = 7$

Total mass: $\mathbf{7.434}$ grams.

(b) Subtract to find the difference:

$3.084 - 1.600 = 1.484$

The second sample is $\mathbf{1.484}$ grams heavier than the third sample.

4. (a) Round $\$ 1.35 $to$ $1$. Estimate:

$\$1 \times 4 = \$4$

(b) Compute $1.35 \times 4$ :

Multiply as whole numbers: $135 \times 4 = 540$ .

$1.35$ has $2$ decimal places, so place the decimal: $5.40$ .

$1.35 \times 4 = 5.40$

The exact cost is $\$ 5.40$.

(c) The estimate was $\$ 4.00 $, and the exact answer is$ $5.40 $. The estimate was$ $5.40 - $4.00 = $1.40 $less than the actual cost. Rounding down by$ $0.35 $per meter added up over$ 4$ meters.

5. (a) Divide $9.6 \div 4$ :

$9.6 \div 4 = 2.4$

Check: $4 \times 2.4 = 9.6$ ✓

Each container gets $\mathbf{2.4}$ liters.

(b) Each container now has the new water plus what was already there:

$2.4 + 0.85 = 3.25$

Each container has $\mathbf{3.25}$ liters.

(c) The leaking container loses $0.375$ liters:

$3.250 - 0.375 = 2.875$

The leaking container has $\mathbf{2.875}$ liters remaining.