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 point.
To compare the value of these numbers using scientific notation, let's write them in that format.
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 10^4 has the least value.
Therefore, the number 12,786 has the least value according to scientific notation.
To compare the values using scientific notation, we need to convert the numbers to scientific notation first.
1) 123,893 = 1.23893 x 10^5
2) 31,892 = 3.1892 x 10^4
3) 12,786 = 1.2786 x 10^4
Now, we can compare the values:
1.23893 x 10^5 > 3.1892 x 10^4 > 1.2786 x 10^4
Therefore, the number 12,786 (1.2786 x 10^4) has the least value when expressed in scientific notation.
To determine which number has the least value using scientific notation, we need to convert each number to scientific notation and compare their exponents.
Let's start with the first number: 123,893.
Step 1: Bring it to a number between 1 and 10 by moving the decimal point. In this case, we can move it to obtain 1.23893.
Step 2: To express this in scientific notation, we need to multiply it by a power of 10. Since we moved the decimal point four places to the left, the exponent will be -4.
Therefore, 123,893 can be written as 1.23893 × 10^4 in scientific notation.
Next, let's convert 31,892.
Step 1: Bring it to a number between 1 and 10. In this case, we can move the decimal point to get 3.1892.
Step 2: We moved the decimal three places to the left, so the exponent will be -3.
Therefore, 31,892 can be written as 3.1892 × 10^3 in scientific notation.
Lastly, let's convert 12,786.
Step 1: Bring it to a number between 1 and 10. In this case, we can move the decimal point to obtain 1.2786.
Step 2: Since we moved the decimal point three places to the left, the exponent will be -3.
Therefore, 12,786 can be written as 1.2786 × 10^4 in scientific notation.
Comparing the exponents of the converted numbers, we see that 123,893 has the highest exponent (-4), followed by 12,786 (-3), and 31,892 (-3).
Therefore, the number with the least value is 31,892 in scientific notation, expressed to the exact decimal point as 3.1892 × 10^3.