Standard Notation Calculator



Write the number 12345.987 in expanded notation form: (Decompose 12345.987)

Remember that each digit in the whole number represents a power of 10:
First take the whole number portion of the number on the left side of the decimal

First, calculate the expanded notation of the whole number portion 12345
Expanded Notation of 12345 = (1 x 104) + (2 x 103) + (3 x 102) + (4 x 101) + (5 x 100)
Expanded Notation of 12345 = (1 x 10000) + (2 x 1000) + (3 x 100) + (4 x 10) + (5 x 1)

Next, calculate the expanded notation of the decimal portion 987
Each decimal place is divided by a power of 10:
Expanded Notation of .987 = (9/101) + (8/102) + (7/103)
Expanded Notation of .987 = (9/10) + (8/100) + (7/1000)

Finally, combine the whole number portion and the decimal portion:
12345.987 = (1 x 10000) + (2 x 1000) + (3 x 100) + (4 x 10) + (5 x 1) + (9/10) + (8/100) + (7/1000)

Now multiply through and simplify to prove this is the correct notation:
12345.987 = (10000 + 2000 + 300 + 40 + 5) + (0.9 + 0.08 + 0.007)
12345.987 = 12345 + . 987
12345.987 = 12345.987 <---- Correct!
(1 x 10000) + (2 x 1000) + (3 x 100) + (4 x 10) + (5 x 1) . (9/10) + (8/100) + (7/1000)