1. Find Convert Decimal to Standard form 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. Find Convert Decimal to Standard form of `123456`
Solution:
`123456`
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 (First number greater than or equal to 1 but less than 10 is 1)
1.23456 (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
`1.23456xx10^5`
`:.123456=1.23456xx10^5`
Other notations:
1. Scientific notation:
`123456 = 1.23456xx10^5`
2. Scientific e notation:
`123456 = 1.23456` e `5`
3. Engineering notation:
`123456 = 123.456 xx 10^3`
4. Normalized notation:
`123456 = 1.23456 xx 10^5`
3. Find Convert Decimal to Standard form of `123.50`
Solution:
`123.50`
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
123.50 (First number greater than or equal to 1 but less than 10 is 1)
1.2350 (Move the decimal point to the left)
Step-2: Count number of decimal places moved
n = 2
Step-3: Write number as product with power of 10
Since we moved the decimal point to the left, so n will be positive
`1.2350xx10^2`
`:.123.50=1.2350xx10^2`
Other notations:
1. Scientific notation:
`123.50 = 1.235xx10^2`
2. Scientific e notation:
`123.50 = 1.235` e `2`
3. Engineering notation:
`123.50 = 123.5 xx 10^0`
4. Normalized notation:
`123.50 = 1.235 xx 10^2`
4. Find Convert Decimal to Standard form of `0.0052`
Solution:
`0.0052`
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
0.0052
0.0052 (First number greater than or equal to 1 but less than 10 is 5)
0005.2 (Move the decimal point to the right after 5)
5.2 (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
`5.2xx10^-3`
`:.0.0052=5.2xx10^-3`
Other notations:
1. Scientific notation:
`0.0052 = 5.2xx10^-3`
2. Scientific e notation:
`0.0052 = 5.2` e `-3`
3. Engineering notation:
`0.0052 = 5.2 xx 10^-3`
4. Normalized notation:
`0.0052 = 5.2 xx 10^-3`
This material is intended as a summary. Use your textbook for detail explanation.
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