1. Convert Decimal notation to Scientific notation of `37000`
Solution:
`37000`
Convert Decimal notation to Scientific notation
Step-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
37000 (First number greater than or equal to 1 but less than 10 is 3)
3.7000 (Move the decimal point to the left)
3.7 (remove trailing zeros)
Step-2: Count number of decimal places moved
n = 4
Step-3: Write number as product with power of 10
Since we moved the decimal point to the left, so n will be positive
`3.7xx10^4`
`:.37000=3.7xx10^4`
Other notations:
1. Scientific notation:
`37000 = 3.7xx10^4`
2. Scientific e notation:
`37000 = 3.7` e `4`
3. Engineering notation:
`37000 = 37 xx 10^3`
4. Normalized notation:
`37000 = 3.7 xx 10^4`
2. Convert Decimal notation to Scientific notation of `123456.7`
Solution:
`123456.7`
Convert Decimal notation to Scientific notation
Step-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
123456.7 (First number greater than or equal to 1 but less than 10 is 1)
1.234567 (Move the decimal point to the left)
Step-2: Count number of decimal places moved
n = 5
Step-3: Write number as product with power of 10
Since we moved the decimal point to the left, so n will be positive
`1.234567xx10^5`
`:.123456.7=1.234567xx10^5`
Other notations:
1. Scientific notation:
`123456.7 = 1.234567xx10^5`
2. Scientific e notation:
`123456.7 = 1.234567` e `5`
3. Engineering notation:
`123456.7 = 123.4567 xx 10^3`
4. Normalized notation:
`123456.7 = 1.234567 xx 10^5`
3. Convert Decimal notation to Scientific notation of `0.0057`
Solution:
`0.0057`
Convert Decimal notation to Scientific notation
Step-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
0.0057
0.0057 (First number greater than or equal to 1 but less than 10 is 5)
0005.7 (Move the decimal point to the right after 5)
5.7 (remove leading zeros)
Step-2: Count number of decimal places moved
n = 3
Step-3: Write number as product with power of 10
Since we moved the decimal point to the right, so n will be negative
`5.7xx10^-3`
`:.0.0057=5.7xx10^-3`
Other notations:
1. Scientific notation:
`0.0057 = 5.7xx10^-3`
2. Scientific e notation:
`0.0057 = 5.7` e `-3`
3. Engineering notation:
`0.0057 = 5.7 xx 10^-3`
4. Normalized notation:
`0.0057 = 5.7 xx 10^-3`
4. Convert Decimal notation to Scientific notation of `123,000,000`
Solution:
`123000000`
Convert Decimal notation to Scientific notation
Step-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
123000000 (First number greater than or equal to 1 but less than 10 is 1)
1.23000000 (Move the decimal point to the left)
1.23 (remove trailing zeros)
Step-2: Count number of decimal places moved
n = 8
Step-3: Write number as product with power of 10
Since we moved the decimal point to the left, so n will be positive
`1.23xx10^8`
`:.123000000=1.23xx10^8`
Other notations:
1. Scientific notation:
`123000000 = 1.23xx10^8`
2. Scientific e notation:
`123000000 = 1.23` e `8`
3. Engineering notation:
`123000000 = 123 xx 10^6`
4. Normalized notation:
`123000000 = 1.23 xx 10^8`
This material is intended as a summary. Use your textbook for detail explanation.
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