Use scientific notation to determine which of these numbers has the least value: 123,893, 31,892, or 12,786. Write your answer in scientific notation, expressed to the exact decimal place
To compare the values of the given numbers using scientific notation, we need to convert them into that form.
First, we will convert the given numbers into scientific notation:
123,893 = 1.23893 x 10^5
31,892 = 3.1892 x 10^4
12,786 = 1.2786 x 10^4
Comparing the exponents, we can see that the smallest value is indicated by the number with the smallest exponent. Therefore, 31,892 (3.1892 x 10^4) has the least value.
To determine which number has the least value, we can convert them into scientific notation. In scientific notation, a number is expressed as a product of a coefficient and a power of 10.
Let's convert each number into scientific notation:
1. 123,893 = 1.23893 × 10^5
2. 31,892 = 3.1892 × 10^4
3. 12,786 = 1.2786 × 10^4
Comparing the exponents in each case, we see that 10^4 is smaller than 10^5. Therefore, 12,786 (1.2786 × 10^4) has the least value.
To determine which number has the least value using scientific notation, we need to convert each of the given numbers into scientific notation.
Let's start with the first number: 123,893.
To express this number in scientific notation, we need to move the decimal point so that we have a number between 1 and 10, multiplied by a power of 10. In this case, since the original number has five digits, we need to move the decimal point five places to the left to obtain a value between 1 and 10.
123,893 = 1.23893 × 10^5
Next, let's convert the second number: 31,892.
Similarly, we need to move the decimal point so that we obtain a number between 1 and 10. In this case, since the original number has four digits, we need to move the decimal point four places to the left.
31,892 = 3.1892 × 10^4
Lastly, let's convert the third number: 12,786.
Again, we need to move the decimal point so that we obtain a number between 1 and 10. In this case, since the original number has four digits, we need to move the decimal point four places to the left.
12,786 = 1.2786 × 10^4
Now, we compare these numbers in scientific notation to determine which one has the least value.
1.23893 × 10^5
3.1892 × 10^4
1.2786 × 10^4
By looking at the coefficients (the numbers before the multiplication sign), we can see that the third number, 1.2786 × 10^4, has the least value.