0.000 550 30 = 5.5030 × 10⁻⁴
Step 1. Identify the significant figures
The important rules are
• Leading zeroes are not significant
• Trapped zeroes between two nonzero digits are significant
• Trailing zeroes after the decimal point are significant
Thus, the underlined digits in 0.000 550 30 are significant.
Step 2. Convert the number to scientific notation.
A number in scientific notation has the form N × 10^a
.
where N is a decimal number called the coefficient and a is an integer called the exponent.
We must have 1 ≤ N < 10
(a) Determine the coefficient
Move the decimal place to the right to create a new number between 1 and 10.
0.000 550 30 → 5.5030; N = 5.5030
(b) Determine the exponent.
The exponent is the number of times you moved the decimal to get the coefficient.
You moved the decimal four places to the right, so the exponent a = -4.
(c) Write the number in scientific notation
0.000 550 30 = N × 10^a = 5.5030 × 10⁻⁴
