When 560,000 is written in scientific notation, the power of 10 is
The Correct Answer and Explanation is:
To write 560,000 in scientific notation, we need to express the number as a product of a coefficient and a power of 10. The general form for scientific notation is:N=C×10nN = C \times 10^nN=C×10n
where:
- NNN is the original number,
- CCC is the coefficient (a number between 1 and 10), and
- nnn is the exponent of 10.
Step 1: Move the Decimal Point
To convert 560,000 into scientific notation, start by moving the decimal point so that there is only one non-zero digit to the left of the decimal point.
- In this case, the decimal point is initially at the end of the number: 560,000.
- We need to move the decimal point 5 places to the left to get the number 5.6, which is between 1 and 10.
Step 2: Count the Number of Places Moved
We moved the decimal point 5 places to the left to get 5.6. This means the power of 10 will be 5, because we moved it five places.
Step 3: Express in Scientific Notation
Now that we know the coefficient is 5.6 and the decimal point was moved 5 places to the left, we can write the number as:560,000=5.6×105560,000 = 5.6 \times 10^5560,000=5.6×105
Thus, the power of 10 in the scientific notation for 560,000 is 5.
Explanation of the Process
Scientific notation is used to express very large or very small numbers in a more compact form. In this case, 560,000 is a relatively large number, so the power of 10 helps us quickly convey how large it is without writing all the zeros. The exponent (5) tells us that the decimal point has been moved five places to the left to transform the number into a form where only one non-zero digit remains before the decimal.
