Answer :
Let's go through the problem step-by-step:
### Part (a)
We need to convert 5600 kilograms (kg) to grams and express it in standard form.
1. Conversion from kilograms to grams:
- We know that there are 1000 grams in 1 kilogram.
- Therefore, to convert kilograms to grams, we multiply the number of kilograms by 1000.
- Calculation: [tex]\(5600 \, \text{kg} \times 1000 = 5600000 \, \text{grams}\)[/tex].
2. Expressing in standard form:
- In standard form, a number is expressed as [tex]\(a \times 10^n\)[/tex], where 1 ≤ [tex]\(a\)[/tex] < 10.
- The number 5600000 grams can be written as [tex]\(5.6 \times 10^6\)[/tex].
So, 5600 kg is [tex]\(5.6 \times 10^6\)[/tex] grams when expressed in standard form.
### Part (b)
We are asked to find how many grains of sand are in 5600 kg of sand, given that each grain weighs approximately [tex]\(8 \times 10^{-5}\)[/tex] grams.
1. Determine the number of grains:
- We need to divide the total weight of the sand in grams by the weight of one grain to find the total number of grains.
- Total weight of the sand in grams is 5600000 grams.
- Weight of one grain is [tex]\(8 \times 10^{-5}\)[/tex] grams.
- Calculation: [tex]\( \frac{5600000}{8 \times 10^{-5}} \)[/tex].
2. Perform the division:
- This calculation gives the result: 70000000000.0.
3. Express in standard form:
- 70000000000.0 can be expressed as [tex]\(7.0 \times 10^{10}\)[/tex] in standard form.
Therefore, there are [tex]\(7.0 \times 10^{10}\)[/tex] grains of sand in 5600 kg of sand.
### Part (a)
We need to convert 5600 kilograms (kg) to grams and express it in standard form.
1. Conversion from kilograms to grams:
- We know that there are 1000 grams in 1 kilogram.
- Therefore, to convert kilograms to grams, we multiply the number of kilograms by 1000.
- Calculation: [tex]\(5600 \, \text{kg} \times 1000 = 5600000 \, \text{grams}\)[/tex].
2. Expressing in standard form:
- In standard form, a number is expressed as [tex]\(a \times 10^n\)[/tex], where 1 ≤ [tex]\(a\)[/tex] < 10.
- The number 5600000 grams can be written as [tex]\(5.6 \times 10^6\)[/tex].
So, 5600 kg is [tex]\(5.6 \times 10^6\)[/tex] grams when expressed in standard form.
### Part (b)
We are asked to find how many grains of sand are in 5600 kg of sand, given that each grain weighs approximately [tex]\(8 \times 10^{-5}\)[/tex] grams.
1. Determine the number of grains:
- We need to divide the total weight of the sand in grams by the weight of one grain to find the total number of grains.
- Total weight of the sand in grams is 5600000 grams.
- Weight of one grain is [tex]\(8 \times 10^{-5}\)[/tex] grams.
- Calculation: [tex]\( \frac{5600000}{8 \times 10^{-5}} \)[/tex].
2. Perform the division:
- This calculation gives the result: 70000000000.0.
3. Express in standard form:
- 70000000000.0 can be expressed as [tex]\(7.0 \times 10^{10}\)[/tex] in standard form.
Therefore, there are [tex]\(7.0 \times 10^{10}\)[/tex] grains of sand in 5600 kg of sand.
