Question

Explain the steps for 0.000000001 in scientific notation

Answer 1

If you count the zeros it’s
one billionth

Answer 2

Answer:

• Find the place value of the most significant digit
• Write the number using that place value as a multiplier
• 1×10^-9

Step-by-step explanation:

It helps immensely if you understand how place value works in a decimal number system. It also helps if you understand the rules of exponents.

Around the decimal point, the place values are ...

  (hundreds) (tens) (ones) . (tenths) (hundredths) (thousandths)

Each location to the right of any given place has a place value that is 1/10 of the one to its left. When there get to be many factors of 10, it is useful to use exponents to represent the repeated multiplication.

  1/10 = 1/10^1

  1/100 = 1/10^2

  1/1000 = 1/10^3

If you count carefully, you find the the digit 1 in your number is in the 9th place to the right of the decimal point, so its multiplier is 1/10^9. That is ...

  0.000000001 = 1/10^9

By the rules of exponents, a positive exponent in the denominator is the same as its opposite exponent in the numerator, so this number can also be written as ...

  0.000000001 = 1×10^-9 . . . . scientific notation