d) $$ \left(3,7 imes 10^{5} ight)-\left(2,5 imes 10^{4} ight) $$ The distance from the Earth to the Sun is 150000000 km . Write the distance in scientific notation. If the speed of sound is $$ 1230 \mathrm{~km} / \mathrm{h} $$, calculate the speed of sound in metres per second. Write your answer correct to the nearest metre.

Question

d) $$ \left(3,7 	imes 10^{5}ight)-\left(2,5 	imes 10^{4}ight) $$ The distance from the Earth to the Sun is 150000000 km . Write the distance in scientific notation. If the speed of sound is $$ 1230 \mathrm{~km} / \mathrm{h} $$, calculate the speed of sound in metres per second. Write your answer correct to the nearest metre.

UpStudy AI · Accepted Answer

Numbers by following steps:
- step0: Solution:
  $$150000000$$
Calculate or simplify the expression $$ 1230 * 1000 / 3600 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1230\times 1000}{3600}$$
- step1: Multiply the numbers:
  $$\frac{1230000}{3600}$$
- step2: Reduce the fraction:
  $$\frac{1025}{3}$$
Calculate or simplify the expression $$ (3.7 * 10^5) - (2.5 * 10^4) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$3.7\times 10^{5}-2.5\times 10^{4}$$
- step1: Rewrite the expression:
  $$370\times 10^{3}-25\times 10^{3}$$
- step2: Collect like terms:
  $$\left(370-25\right)\times 10^{3}$$
- step3: Subtract the numbers:
  $$345\times 10^{3}$$
- step4: Evaluate the power:
  $$345\times 1000$$
- step5: Multiply the numbers:
  $$345000$$
Let's break down the problem step by step.

1. **Calculating $$ (3.7 \times 10^5) - (2.5 \times 10^4) $$**:
   - First, we need to express both numbers in the same power of ten. 
   - $$ 2.5 \times 10^4 $$ can be rewritten as $$ 0.25 \times 10^5 $$.
   - Now we can perform the subtraction:
     $$
     (3.7 \times 10^5) - (0.25 \times 10^5) = (3.7 - 0.25) \times 10^5 = 3.45 \times 10^5
     $$
   - The result in decimal form is $$ 345000 $$.

2. **Writing the distance from the Earth to the Sun in scientific notation**:
   - The distance is given as $$ 150000000 $$ km.
   - In scientific notation, this is expressed as:
     $$
     1.5 \times 10^8 \text{ km}
     $$

3. **Calculating the speed of sound in meters per second**:
   - The speed of sound is given as $$ 1230 \text{ km/h} $$.
   - To convert this to meters per second, we use the conversion factor $$ 1 \text{ km} = 1000 \text{ m} $$ and $$ 1 \text{ hour} = 3600 \text{ seconds} $$:
     $$
     \text{Speed in m/s} = \frac{1230 \times 1000}{3600}
     $$
   - This simplifies to approximately $$ 341.67 \text{ m/s} $$, which rounds to $$ 342 \text{ m/s} $$ when rounded to the nearest meter.

### Summary of Results:
- The result of $$ (3.7 \times 10^5) - (2.5 \times 10^4) $$ is $$ 345000 $$.
- The distance from the Earth to the Sun in scientific notation is $$ 1.5 \times 10^8 $$ km.
- The speed of sound in meters per second is approximately $$ 342 \text{ m/s} $$.
$$ (3.7 \times 10^5) - (2.5 \times 10^4) = 345000 $$ Distance from Earth to the Sun: $$ 1.5 \times 10^8 $$ km Speed of sound: $$ 342 $$ m/s

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