1. Example-1
1. Find Convert Standard form to Decimal form of `6.2*10^3`
Solution:
`6.2 xx 10^3`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=3`
Step-2: n is positive, so move the decimal point 3 places to the right
6.2
6.2 (3 places to the right)
6.2 0 0 (add zeros)
6200 (Move the decimal point 3 places)
`:.6.2 xx 10^3=6200`
Method-2:
`6.2 xx 10^3=6.2 xx 1000=6200`
Other notations:
1. Scientific notation:
`6200 = 6.2xx10^3`
2. Scientific e notation:
`6200 = 6.2` e `3`
3. Engineering notation:
`6200 = 6.2 xx 10^3`
4. Normalized notation:
`6200 = 6.2 xx 10^3`
2. Find Convert Standard form to Decimal form of `6.212589*10^4`
Solution:
`6.212589 xx 10^4`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=4`
Step-2: n is positive, so move the decimal point 4 places to the right
6.212589
6.2 1 2 5 89 (4 places to the right)
62125.89 (Move the decimal point 4 places)
`:.6.212589 xx 10^4=62125.89`
Method-2:
`6.212589 xx 10^4=6.212589 xx 10000=62125.89`
Other notations:
1. Scientific notation:
`62125.89 = 6.212589xx10^4`
2. Scientific e notation:
`62125.89 = 6.212589` e `4`
3. Engineering notation:
`62125.89 = 62.12589 xx 10^3`
4. Normalized notation:
`62125.89 = 6.212589 xx 10^4`
3. Find Convert Standard form to Decimal form of `0.000089*10^3`
Solution:
`0.000089 xx 10^3`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=3`
Step-2: n is positive, so move the decimal point 3 places to the right
0.000089
0.0 0 0 089 (3 places to the right)
0000.089 (Move the decimal point 3 places)
0.089 (remove leading zeros)
`:.0.000089 xx 10^3=0.089`
Method-2:
`0.000089 xx 10^3=0.000089 xx 1000=0.089`
Other notations:
1. Scientific notation:
`0.089 = 8.9xx10^-2`
2. Scientific e notation:
`0.089 = 8.9` e `-2`
3. Engineering notation:
`0.089 = 89 xx 10^-3`
4. Normalized notation:
`0.089 = 8.9 xx 10^-2`
4. Find Convert Standard form to Decimal form of `12345678*10^-5`
Solution:
`12345678 xx 10^-5`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=-5`
Step-2: n is negative, so move the decimal point 5 places to the left
12345678
1234 5 6 7 8 (5 places to the left)
123.45678 (Move the decimal point 5 places)
`:.12345678 xx 10^-5=123.45678`
Method-2:
`12345678 xx 10^-5=12345678 xx 0.00001=123.45678`
Other notations:
1. Scientific notation:
`123.45678 = 1.2345678xx10^2`
2. Scientific e notation:
`123.45678 = 1.2345678` e `2`
3. Engineering notation:
`123.45678 = 123.45678 xx 10^0`
4. Normalized notation:
`123.45678 = 1.2345678 xx 10^2`
5. Find Convert Standard form to Decimal form of `8.9*10^-3`
Solution:
`8.9 xx 10^-3`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=-3`
Step-2: n is negative, so move the decimal point 3 places to the left
8.9
8 .9 (3 places to the left)
0 0 8 .9 (add zeros)
0.0089 (Move the decimal point 3 places)
`:.8.9 xx 10^-3=0.0089`
Method-2:
`8.9 xx 10^-3=8.9 xx 0.001=0.0089`
Other notations:
1. Scientific notation:
`0.0089 = 8.9xx10^-3`
2. Scientific e notation:
`0.0089 = 8.9` e `-3`
3. Engineering notation:
`0.0089 = 8.9 xx 10^-3`
4. Normalized notation:
`0.0089 = 8.9 xx 10^-3`
6. Find Convert Standard form to Decimal form of `500*10^-4`
Solution:
`500 xx 10^-4`
Convert Scientific notation to Decimal notation
Step-1: Find the exponent n to the power of 10
`n=-4`
Step-2: n is negative, so move the decimal point 4 places to the left
500
5 0 0 (4 places to the left)
0 5 0 0 (add zeros)
0.0500 (Move the decimal point 4 places)
0.05 (remove trailing zeros)
`:.500 xx 10^-4=0.05`
Method-2:
`500 xx 10^-4=500 xx 0.0001=0.05`
Other notations:
1. Scientific notation:
`0.05 = 5xx10^-2`
2. Scientific e notation:
`0.05 = 5` e `-2`
3. Engineering notation:
`0.05 = 50 xx 10^-3`
4. Normalized notation:
`0.05 = 5 xx 10^-2`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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