Question

convert the following to scientific notation.

1. 0.005 =
2. 5,050 =
3. 0.0008 =
4. 1,000 =
5. 1,000,000 =
6. 0.25 =
7. 0.025 =
8. 0.0025 =
9. 500 =
10. 5,000 =

Explanation:

Step1: Recall scientific - notation form

Scientific notation is $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Convert 0.005

Move the decimal point 3 places to the right to get $a = 5$. Since we moved the decimal point 3 places to the right, $n=-3$. So, $0.005 = 5\times10^{-3}$.

Step3: Convert 5050

Move the decimal point 3 places to the left to get $a = 5.05$. Since we moved the decimal point 3 places to the left, $n = 3$. So, $5050=5.05\times10^{3}$.

Step4: Convert 0.0008

Move the decimal point 4 places to the right to get $a = 8$. Since we moved the decimal point 4 places to the right, $n=-4$. So, $0.0008 = 8\times10^{-4}$.

Step5: Convert 1000

Move the decimal point 3 places to the left to get $a = 1$. Since we moved the decimal point 3 places to the left, $n = 3$. So, $1000=1\times10^{3}$.

Step6: Convert 1000000

Move the decimal point 6 places to the left to get $a = 1$. Since we moved the decimal point 6 places to the left, $n = 6$. So, $1000000=1\times10^{6}$.

Step7: Convert 0.25

Move the decimal point 1 place to the right to get $a = 2.5$. Since we moved the decimal point 1 place to the right, $n=-1$. So, $0.25 = 2.5\times10^{-1}$.

Step8: Convert 0.025

Move the decimal point 2 places to the right to get $a = 2.5$. Since we moved the decimal point 2 places to the right, $n=-2$. So, $0.025 = 2.5\times10^{-2}$.

Step9: Convert 0.0025

Move the decimal point 3 places to the right to get $a = 2.5$. Since we moved the decimal point 3 places to the right, $n=-3$. So, $0.0025 = 2.5\times10^{-3}$.

Step10: Convert 500

Move the decimal point 2 places to the left to get $a = 5$. Since we moved the decimal point 2 places to the left, $n = 2$. So, $500=5\times10^{2}$.

Step11: Convert 5000

Move the decimal point 3 places to the left to get $a = 5$. Since we moved the decimal point 3 places to the left, $n = 3$. So, $5000=5\times10^{3}$.

Answer:

1. $5\times10^{-3}$
2. $5.05\times10^{3}$
3. $8\times10^{-4}$
4. $1\times10^{3}$
5. $1\times10^{6}$
6. $2.5\times10^{-1}$
7. $2.5\times10^{-2}$
8. $2.5\times10^{-3}$
9. $5\times10^{2}$
10. $5\times10^{3}$