Question

Write in standard form
1 : 0.000000009
2:0.00012
3: 1275000000

Please give step by step

Answer 1

In standard form, a number is written in the form of $a \times 10^b$

here, a is a real number between 1 and 10 and b is an integer.

● If a number is greater than 1; b is non-negative. That means b can be either 0 or a positive integer.
● If the number is less than 1; then in standard form, b is a negative integer.


$1) \: \: 0.000000009 = \frac{9}{1000000000} \\ \\ = \frac{9}{10^9} = 9 \times {10}^{ - 9} \\ \\ \\ 2) \: \: 0.00012 = \frac{12}{100000} \\ \\ = \frac{12}{10^5} = 12 \times 10^{-5}= 1.2 \times {10}^{ - 4} \\ \\ \\ 3) \: \: 1275000000 = 1.275 \times 1000000000 = 1.275 \times {10}^{9}$

Answer 2

$\huge\bold\color {green}{Hello \: Friend \: !!}$

$\red {\bold {Here \: is \: your \: answer}}$

$\underline\bold {Question : Write \: in \: standard \: form}$

$\bold {1. \: 0.000000009}$

$\bold {↪ Standard \: form = 9 × 10^{ - 9} }$

↪ Here I have putted ( - 9 ) as power, because after the point there are 9 numbers and it is after point so I putted minus sign.

$\bold {2. \: 0.00012}$

$\bold {↪ Standard \: form = 1.2 × 10^{ - 4} }$

↪ Here there are 5 numbers after the point, even though there are 5 numbers, we should count up to 1 only.

↪ I will give you another example.

▶ Example : 0.00345

↪ Answer : 3.45 × 10^-3

↪ Even though there are 5 numbers after the point, we should count upto 3 only.

$\bold {3. \: 1275000000}$

$\bold {↪ Standard \: form = 1.275 × 10 ^{9} }$

↪ Here there are 9 numbers after 1, and there is no point before, so the power is positive.

$\mathbb{\huge {\fcolorbox{yellow}{green}{Hope It Helps}}}$