1. Standard form of a number of `37000`Solution:`37000`
The standard form of a number is also known as scientific notation of a number
`37000`
Convert Decimal notation to Scientific notationStep-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`
Standard form of `37000` is `3.7xx10^4`
2. Standard form of a number of `123456.7`Solution:`123456.7`
The standard form of a number is also known as scientific notation of a number
`123456.7`
Convert Decimal notation to Scientific notationStep-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`
Standard form of `123456.7` is `1.234567xx10^5`
3. Standard form of a number of `0.0000567`Solution:`0.0000567`
The standard form of a number is also known as scientific notation of a number
`0.0000567`
Convert Decimal notation to Scientific notationStep-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
0.0000567
0.0000567 (First number greater than or equal to 1 but less than 10 is 5)
0
00005.67 (Move the decimal point to the right after 5)
5.67 (remove leading zeros)
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 right, so n will be negative
`5.67xx10^-5`
`:.0.0000567=5.67xx10^-5`
Standard form of `0.0000567` is `5.67xx10^-5`
4. Standard form of a number of `123,000,000,000`Solution:`123,000,000,000`
The standard form of a number is also known as scientific notation of a number
`123000000000`
Convert Decimal notation to Scientific notationStep-1: Move decimal point, so that first number is greater than or equal to 1 but less than 10
123000000000 (First number greater than or equal to 1 but less than 10 is 1)
1.
23000000000 (Move the decimal point to the left)
1.23 (remove trailing zeros)
Step-2: Count number of decimal places moved
n = 11
Step-3: Write number as product with power of 10
Since we moved the decimal point to the left, so n will be positive
`1.23xx10^11`
`:.123000000000=1.23xx10^11`
Standard form of `123,000,000,000` is `1.23xx10^11`