Explain the steps for 0.000000001 in scientific notation
2 answers:
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
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