What is the order of
1.5 x 10^3, 1.4 x 10^-1, 2 x 10^3, and 1.4 x 1-^-2 from least to greatest?
Online, "^" is used to designate an exponent, because it avoids the confusion with x being used as an unknown.
I assume the first dash in the last term was supposed to be a zero. In ascending order, they are:
1.4 * 10^-2
1.4 * 10^-1
1.5 * 10^3
2 * 10^3
Ah, I see we're playing with some powers of ten. To arrange them from least to greatest, let's have some numerical fun!
First, let's bring those powers of ten to the same level.
1.5 x 10^3 = 1500
2 x 10^3 = 2000
Now let's deal with those negative exponents:
1.4 x 10^-1 = 0.14
1.4 x 1^-^-2 = 1.4
So now we have: 0.14, 1.4, 1500, 2000
Now let's put these numbers in order from least to greatest based on their value:
0.14, 1.4, 1500, 2000
And there we have it! From least to greatest: 0.14, 1.4, 1500, 2000.
To determine the order of the given numbers from least to greatest, we need to compare the exponents first.
The exponents in order are as follows:
1.4 x 10^-1 (negative exponent: smallest)
1.4 x 10^-2 (negative exponent: second smallest)
1.5 x 10^3 (positive exponent: second largest)
2 x 10^3 (positive exponent: largest)
Now, we compare the numbers with the same exponent values.
Considering the two numbers with a negative exponent:
1.4 x 10^-2 is smaller than 1.4 x 10^-1
Therefore, the order becomes:
1.4 x 10^-2, 1.4 x 10^-1
Considering the two numbers with a positive exponent:
1.5 x 10^3 is smaller than 2 x 10^3
Therefore, the order becomes:
1.4 x 10^-2, 1.4 x 10^-1, 1.5 x 10^3, 2 x 10^3
In conclusion, the order from least to greatest is:
1.4 x 10^-2, 1.4 x 10^-1, 1.5 x 10^3, 2 x 10^3.
To determine the order of the numbers, we need to compare their values without the scientific notation. Here's how you can do it:
1. Convert the numbers from scientific notation to standard form:
- 1.5 x 10^3 = 1500
- 1.4 x 10^-1 = 0.14 (since the exponent is negative, you move the decimal point to the left)
- 2 x 10^3 = 2000
- 1.4 x 10^-2 = 0.014
2. Arrange the numbers in ascending order from least to greatest:
- 0.014, 0.14, 1500, 2000
Therefore, the numbers in ascending order from least to greatest are: 0.014, 0.14, 1500, 2000.