1. Example-1
1. Convert Scientific notation to Decimal notation 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. Convert Scientific notation to Decimal notation of `1.2345678*10^4`
Solution:
`1.2345678 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
1.2345678
1.2 3 4 5 678 (4 places to the right)
12345.678 (Move the decimal point 4 places)
`:.1.2345678 xx 10^4=12345.678`
Method-2:
`1.2345678 xx 10^4=1.2345678 xx 10000=12345.678`
Other notations:
1. Scientific notation:
`12345.678 = 1.2345678xx10^4`
2. Scientific e notation:
`12345.678 = 1.2345678` e `4`
3. Engineering notation:
`12345.678 = 12.345678 xx 10^3`
4. Normalized notation:
`12345.678 = 1.2345678 xx 10^4`
3. Convert Scientific notation to Decimal notation 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. Convert Scientific notation to Decimal notation of `6.7*10^-5`
Solution:
`6.7 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
6.7
6 .7 (5 places to the left)
0 0 0 0 6 .7 (add zeros)
0.000067 (Move the decimal point 5 places)
`:.6.7 xx 10^-5=0.000067`
Method-2:
`6.7 xx 10^-5=6.7 xx 0.00001=0.000067`
Other notations:
1. Scientific notation:
`0.000067 = 6.7xx10^-5`
2. Scientific e notation:
`0.000067 = 6.7` e `-5`
3. Engineering notation:
`0.000067 = 67 xx 10^-6`
4. Normalized notation:
`0.000067 = 6.7 xx 10^-5`
5. Convert Scientific notation to Decimal notation of `50*10^-4`
Solution:
`50 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
50
5 0 (4 places to the left)
0 0 5 0 (add zeros)
0.0050 (Move the decimal point 4 places)
0.005 (remove trailing zeros)
`:.50 xx 10^-4=0.005`
Method-2:
`50 xx 10^-4=50 xx 0.0001=0.005`
Other notations:
1. Scientific notation:
`0.005 = 5xx10^-3`
2. Scientific e notation:
`0.005 = 5` e `-3`
3. Engineering notation:
`0.005 = 5 xx 10^-3`
4. Normalized notation:
`0.005 = 5 xx 10^-3`
6. Convert Scientific notation to Decimal notation of `123456.7*10^-3`
Solution:
`123456.7 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
123456.7
1234 5 6 .7 (3 places to the left)
123.4567 (Move the decimal point 3 places)
`:.123456.7 xx 10^-3=123.4567`
Method-2:
`123456.7 xx 10^-3=123456.7 xx 0.001=123.4567`
Other notations:
1. Scientific notation:
`123.4567 = 1.234567xx10^2`
2. Scientific e notation:
`123.4567 = 1.234567` e `2`
3. Engineering notation:
`123.4567 = 123.4567 xx 10^0`
4. Normalized notation:
`123.4567 = 1.234567 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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