If a raindrop weighs 160 mg (milligram) on average and $$ 2.6 imes 10^{3} $$ raindrops fall on the lawn every 10 minutes, what mass in kilogram $$ (\mathrm{kg} $$ ) of rain falls on the lawn in 6 mins? (Answer to I decimal place)

Question

If a raindrop weighs 160 mg (milligram) on average and $$ 2.6 	imes 10^{3} $$ raindrops fall on the lawn every 10 minutes, what mass in kilogram $$ (\mathrm{kg} $$ ) of rain falls on the lawn in 6 mins? (Answer to I decimal place)

UpStudy AI · Accepted Answer

To find the mass of rain that falls on the lawn in 6 minutes, we can follow these steps:

1. **Calculate the number of raindrops that fall in 6 minutes.**
   - We know that $$ 2.6 \times 10^{3} $$ raindrops fall every 10 minutes.
   - Therefore, in 1 minute, the number of raindrops that fall is:
     $$
     \text{Raindrops per minute} = \frac{2.6 \times 10^{3}}{10}
     $$
   - In 6 minutes, the total number of raindrops is:
     $$
     \text{Total raindrops in 6 minutes} = \text{Raindrops per minute} \times 6
     $$

2. **Calculate the total mass of the raindrops in milligrams.**
   - Each raindrop weighs 160 mg, so the total mass in milligrams is:
     $$
     \text{Total mass (mg)} = \text{Total raindrops in 6 minutes} \times 160
     $$

3. **Convert the total mass from milligrams to kilograms.**
   - Since $$ 1 \, \text{kg} = 10^{6} \, \text{mg} $$, we convert the mass to kilograms by dividing by $$ 10^{6} $$.

Now, let's perform the calculations step by step.

### Step 1: Calculate the number of raindrops in 6 minutes
$$
\text{Raindrops per minute} = \frac{2.6 \times 10^{3}}{10} = 2.6 \times 10^{2}
$$
$$
\text{Total raindrops in 6 minutes} = 2.6 \times 10^{2} \times 6
$$

### Step 2: Calculate the total mass in milligrams
$$
\text{Total mass (mg)} = \text{Total raindrops in 6 minutes} \times 160
$$

### Step 3: Convert to kilograms
$$
\text{Total mass (kg)} = \frac{\text{Total mass (mg)}}{10^{6}}
$$

Now, let's calculate these values.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{2.6\times 10^{3}}{10}\times 6$$
- step1: Reduce the fraction:
  $$2.6\times 10^{2}\times 6$$
- step2: Rewrite the expression:
  $$26\times 10\times 6$$
- step3: Multiply the terms:
  $$260\times 6$$
- step4: Multiply the numbers:
  $$1560$$
Calculate or simplify the expression $$ 160 * ((2.6 * 10^3) / 10 * 6) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$160\left(\frac{2.6\times 10^{3}}{10}\times 6\right)$$
- step1: Remove the parentheses:
  $$160\times \frac{2.6\times 10^{3}}{10}\times 6$$
- step2: Reduce the fraction:
  $$160\times 2.6\times 10^{2}\times 6$$
- step3: Multiply the terms:
  $$2496\times 10^{2}$$
- step4: Evaluate the power:
  $$2496\times 100$$
- step5: Multiply:
  $$249600$$
Calculate or simplify the expression $$ 249600 / 10^6 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{249600}{10^{6}}$$
- step1: Rewrite the expression:
  $$\frac{100\times 2496}{10^{6}}$$
- step2: Rewrite the expression:
  $$\frac{10^{2}\times 2496}{10^{6}}$$
- step3: Reduce the fraction:
  $$\frac{2496}{10^{4}}$$
- step4: Rewrite the expression:
  $$\frac{64\times 39}{10^{4}}$$
- step5: Rewrite the expression:
  $$\frac{64\times 39}{2^{4}\times 5^{4}}$$
- step6: Rewrite the expression:
  $$\frac{2^{6}\times 39}{2^{4}\times 5^{4}}$$
- step7: Reduce the fraction:
  $$\frac{2^{2}\times 39}{5^{4}}$$
- step8: Calculate:
  $$\frac{156}{5^{4}}$$
- step9: Evaluate the power:
  $$\frac{156}{625}$$
Let's summarize the calculations:

1. **Total raindrops in 6 minutes:**
   $$
   \text{Total raindrops in 6 minutes} = 1560
   $$

2. **Total mass in milligrams:**
   $$
   \text{Total mass (mg)} = 160 \times 1560 = 249600 \, \text{mg}
   $$

3. **Convert to kilograms:**
   $$
   \text{Total mass (kg)} = \frac{249600}{10^{6}} = 0.2496 \, \text{kg}
   $$

Finally, rounding to one decimal place, the mass of rain that falls on the lawn in 6 minutes is:
$$
\text{Mass} \approx 0.2 \, \text{kg}
$$

Thus, the answer is $$ 0.2 \, \text{kg} $$.
The mass of rain that falls on the lawn in 6 minutes is approximately 0.2 kg.

If a raindrop weighs 160 mg (milligram) on average and \( 2.6 \times 10^{3} \) raindrops fall on the lawn every 10 minutes, what mass in kilogram \( (\mathrm{kg} \) ) of rain falls on the lawn in 6 mins? (Answer to I decimal place)

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