Question #a4616
1 Answer
The correct way is the other way around.
Consider the number 200.
We can write this as 2 × 10 × 10 or 2 × 10².
We can write 200 as 200 × 10⁰ or 20 × 10¹ or 2 × 10².
Each time we move the decimal point one place to the left, the exponent increases by 1.
In standard scientific notation, we write only one nonzero digit to the left of the decimal point.
To change from decimal to standard notation:
- Place the decimal point so that there is one non-zero digit to the left of the decimal point.
- Count the number of decimal places the decimal has moved from the original number. This will be the exponent of the 10.
- If we move the exponent to the left, the exponent is positive; if we move the exponent to the right, the exponent is negative.
EXAMPLE
Convert the numbers (a) 4 750 000 and (b) 0.000 789 to standard scientific notation.
(a) Write the number as 4.75. We moved the decimal point 6 places to the left, so the exponent is positive. The number becomes 4.74 × 10⁶.
(b) Write the number as 7.89. We moved the decimal point 4 places to the right, so the exponent is negative. The number becomes 7.89 × 10⁻⁴.
