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Scientific Notation Calculator
Convert a decimal to scientific notation, turn a power of 10 back into a decimal, and write expanded form. Steps count how far the decimal point moves.
A plain decimal, up to 20 significant digits.
Enter a decimal number, such as 5400 or 0.00032.
Formula
a × 10^n, where 1 ≤ |a| < 10, and n is an integer.
Enter a decimal number, such as 5400 or 0.00032.
This scientific notation calculator rewrites a decimal as a coefficient times a power of 10, and it turns a coefficient and an exponent back into a decimal string. The coefficient a satisfies 1 ≤ |a| < 10: ignoring its sign, it is at least 1 and less than 10. A negative number keeps its minus sign on the coefficient, and a number between 0 and 1, or between −1 and 0, gets a negative exponent. The steps count how many places the decimal point moved. A third mode writes an integer or a decimal in expanded form, so 345.6 becomes 3×100 + 4×10 + 5×1 + 6×0.1.
How the decimal point moves
To write a decimal in scientific notation, slide the decimal point until one non-zero digit stands in front of it. The number of places you slide is the exponent. Sliding left makes the exponent positive. Numbers that are 10 or larger, such as 5400, need that leftward slide: the decimal point starts after the last digit and slides 3 places left to make 5.4, so 5400 = 5.4 × 10^3.
Numbers greater than 0 and less than 1 slide the decimal point to the right, and that makes the exponent negative. In 0.00032 the first non-zero digit is 3, four places to the right of the decimal point, so 0.00032 = 3.2 × 10^-4. To go from scientific notation back to a decimal, move the point the number of places in the exponent: 6.02 × 10^23 moves 23 places to the right and fills the empty places with zeros. A number that is already at least 1 and less than 10 has exponent 0, because 10^0 equals 1.
Expanded form
Expanded form writes each digit times its place value and adds those products. 345.6 is 3 hundreds, 4 tens, 5 ones, and 6 tenths, which is 3×100 + 4×10 + 5×1 + 6×0.1, or 300 + 40 + 5 + 0.6. A whole number such as 345 stops at the ones place. This mode stays with numbers you can read place by place: up to nine digits before the decimal point and six after it.
Frequently Asked Questions
What is scientific notation?
Scientific notation writes a number as a coefficient times a power of 10. The coefficient a satisfies 1 ≤ |a| < 10: ignoring its sign, it is at least 1 and less than 10. The exponent is an integer: positive when the size is 10 or larger, negative when the number is between 0 and 1 or between −1 and 0, and 0 when the number already sits in that coefficient range.
How do you convert 0.00032 to scientific notation?
Move the decimal point right until it sits after the 3. That move is 4 places, and a move to the right makes the exponent negative. So 0.00032 = 3.2 × 10^-4.
How do you turn 6.02 × 10^23 into a decimal?
The exponent 23 says to move the decimal point in 6.02 twenty-three places to the right. The digits become 602, and the other 21 places are zeros. The decimal is 602 followed by 21 zeros.
How do you write 345.6 in expanded form?
Multiply each digit by its place value and add the products. 345.6 is 3×100 + 4×10 + 5×1 + 6×0.1, which is 300 + 40 + 5 + 0.6.
Where does the minus sign go on a negative number?
The minus sign stays on the coefficient. −5400 is −5.4 × 10^3, and −0.00032 is −3.2 × 10^-4. The exponent matches the exponent of the positive number with the same digits.