How do you convert a small number to scientific notation?

How do you convert a small number to scientific notation?

• A. Move the decimal point to the right
• B. Multiply by 10 until greater than 1
• C. Write as a sum of powers of ten
• D. Write it as a division problem, then convert to multiplication with a negative exponent

Answer: (D)

To express a small number in scientific notation, you want a coefficient between 1 and 10 multiplied by a power of ten, where the exponent is negative for numbers less than 1. A clear way is to write the number as a division by a power of ten, then convert that division into a multiplication by a negative exponent. For example, 0.0034 can be written as 3.4 ÷ 1000, which equals 3.4 × 10^-3. This directly shows the coefficient (3.4) and the negative exponent corresponding to how far the decimal must move to place the coefficient between 1 and 10. The other approaches are less precise. Moving the decimal point alone doesn’t finalize the standard form. Multiplying by 10 until you exceed 1 can work in principle but doesn’t by itself show how the exponent should be written. Writing as a sum of powers of ten isn’t the standard scientific notation form.

To express a small number in scientific notation, you want a coefficient between 1 and 10 multiplied by a power of ten, where the exponent is negative for numbers less than 1. A clear way is to write the number as a division by a power of ten, then convert that division into a multiplication by a negative exponent. For example, 0.0034 can be written as 3.4 ÷ 1000, which equals 3.4 × 10^-3. This directly shows the coefficient (3.4) and the negative exponent corresponding to how far the decimal must move to place the coefficient between 1 and 10.

The other approaches are less precise. Moving the decimal point alone doesn’t finalize the standard form. Multiplying by 10 until you exceed 1 can work in principle but doesn’t by itself show how the exponent should be written. Writing as a sum of powers of ten isn’t the standard scientific notation form.