1.3.2 Standard Form
1.3.2 Standard Form
It is a convenient way to read and write very big or very small numbers.
Numbers like \( 1657385000000 \) or \( 0.0000000586 \) are difficult to read and understand.
Therefore, we write such numbers in standard form, which is \( a \times 10^n \)
Where a is a number between \( 1 \) and \( 10 \)
\( n \) is positive for large numbers
\( n \) is negative for small numbers
The standard forms of the above numbers are \( 1.657385 \times 10^{(12)} \) and \( 5.86 \times 10^ {(-8)} \) respectively.
Worked Example:
Write \( 968260000000 \) in standard form.
Write first non zero digit
\( 9 \)
After that, add a decimal point and write the remaining non-zero values.
\( 9.6826 \)
Count the number of digits after \( 9 \) now.
\( 968260000000 \) , there are \( 11 \) digits.
So, the value of \( n \) is \( 11 \).
\( 9.6826 \times 10^{(11)} \)
\( 968260000000=9.6826 \times 10^{(11)} \)
Tip:
Verify your answer by calculator.
Worked Example:
Write \( 0.000005042 \) in standard form.
Write first non zero digit
\( 5 \)
After that, add a decimal point and write the remaining values.
\( 5.042 \)
Notice that the decimal point shifts 6 places to the right.
Therefore, the value of \( n \) is \( -6 \)
\( 5.042 \times 10^{(-6)} \)
\( 0.000005042=5.042 \times 10^{(-6)} \)
Tip:
Verify your answer by calculator.
Test yourself
Question 1:
Write \( 73 \) million in standard form.
[1]
Question 2:
The earth has a surface area of approximately \( 510100000 km^2 \).
Write this surface area in standard form.
[1]
Question 3:
Write \( 0.000573 \) in standard form.
[1]