Question

scientists very often deal with very small and very large numbers, which can lead to a lot of confusion when counting zeros! we have learned to express these numbers as powers of 10.
scientific notation takes the form of m x 10^n where 1 ≤ m < 10 and n represents the number of decimal places to be moved. positive n indicates the standard form is larger than zero, whereas negative n would indicate a number smaller than zero.
example 1: convert 1,500,000 to scientific notation.
move the decimal point so that there is only one digit to its left, a total of 6 places.
1,500,000 = 1.5 x 10^6
example 2: convert 0.00025 to scientific notation.
for this, move the decimal point 4 places to the right.
0.00025 = 2.5 x 10^(-4)
(note that when a number starts out less than one, the exponent is always negative.)
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 =

convert the following to standard notation.

1. 1.5 x 10^3 =
2. 1.5 x 10^(-3) =
3. 3.75 x 10^(-2) =
4. 3.75 x 10^2 =
5. 2.2 x 10^5 =
6. 3.35 x 10^(-1) =
7. 1.2 x 10^(-4) =
8. 1 x 10^4 =
9. 1 x 10^(-1) =
10. 4 x 10^0 =

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $M\times10^{n}$ where $1\leq M<10$ and $n$ is an integer representing the number of decimal - places moved.

Step2: Convert numbers to scientific notation

For 0.005:

Move the decimal point 3 places to the right. So, $0.005 = 5\times10^{-3}$.

For 5.050:

It is already in a form close to scientific notation. $5.050=5.05\times 10^{0}$.

For 0.0008:

Move the decimal point 4 places to the right. So, $0.0008 = 8\times10^{-4}$.

For 1.000:

$1.000 = 1\times10^{0}$.

For 1,000,000:

Move the decimal point 6 places to the left. So, $1000000 = 1\times10^{6}$.

For 0.25:

Move the decimal point 1 place to the right. So, $0.25 = 2.5\times10^{-1}$.

For 0.025:

Move the decimal point 2 places to the right. So, $0.025 = 2.5\times10^{-2}$.

For 0.0025:

Move the decimal point 3 places to the right. So, $0.0025 = 2.5\times10^{-3}$.

For 500:

Move the decimal point 2 places to the left. So, $500 = 5\times10^{2}$.

For 5,000:

Move the decimal point 3 places to the left. So, $5000 = 5\times10^{3}$.

Step3: Convert numbers from scientific notation to standard notation

For $1.5\times10^{3}$:

Move the decimal point 3 places to the right. So, $1.5\times10^{3}=1500$.

For $1.5\times10^{-3}$:

Move the decimal point 3 places to the left. So, $1.5\times10^{-3}=0.0015$.

For $3.75\times10^{-2}$:

Move the decimal point 2 places to the left. So, $3.75\times10^{-2}=0.0375$.

For $3.75\times10^{2}$:

Move the decimal point 2 places to the right. So, $3.75\times10^{2}=375$.

For $2.2\times10^{5}$:

Move the decimal point 5 places to the right. So, $2.2\times10^{5}=220000$.

For $3.35\times10^{-1}$:

Move the decimal point 1 place to the left. So, $3.35\times10^{-1}=0.335$.

For $1.2\times10^{-4}$:

Move the decimal point 4 places to the left. So, $1.2\times10^{-4}=0.00012$.

For $1\times10^{4}$:

Move the decimal point 4 places to the right. So, $1\times10^{4}=10000$.

For $1\times10^{-1}$:

Move the decimal point 1 place to the left. So, $1\times10^{-1}=0.1$.

For $4\times10^{0}$:

Since any non - zero number to the power of 0 is 1, $4\times10^{0}=4$.

Answer:

1. $5\times10^{-3}$
2. $5.05\times10^{0}$
3. $8\times10^{-4}$
4. $1\times10^{0}$
5. $1\times10^{6}$
6. $2.5\times10^{-1}$
7. $2.5\times10^{-2}$
8. $2.5\times10^{-3}$
9. $5\times10^{2}$
10. $5\times10^{3}$
11. $1500$
12. $0.0015$
13. $0.0375$
14. $375$
15. $220000$
16. $0.335$
17. $0.00012$
18. $10000$
19. $0.1$
20. $4$