Question

What is the order of 4*10⁻⁷, 7*10⁻⁹,1*10⁴, 2*10⁴ from least to greatest

Answer 1

The order from least to greatest for the numbers 4∗10⁻⁷, 7∗10⁻⁹, 1∗10⁴, 2∗10⁴ is 7∗10⁻⁹, 4∗10⁻⁷, 1∗10⁴, 2∗10⁴, based on the magnitude of their exponents in scientific notation.

Step-by-step explanation:

To put the numbers 4∗10⁻⁷, 7∗10⁻⁹, 1∗10⁴, 2∗10⁴ in order from least to greatest, we need to understand their magnitude based on the exponents of ten. The negative exponents indicate numbers smaller than one, and the larger the negative exponent, the smaller the number. The positive exponents indicate numbers larger than one, with larger positive exponents representing larger numbers.

Here is the order from least to greatest:

1. 7∗10⁻⁹ (This is the smallest because it has the largest negative exponent.)
2. 4∗10⁻⁷ (This is larger than 7∗10⁻⁹ but still less than one.)
3. 1∗10⁴ (This is larger than any of the negative exponents and is a positive ten thousand.)
4. 2∗10⁴ (This is the largest number, doubling the previous one.)

Remember, in scientific notation, a negative exponent means the number is a fraction (less than one) and a positive exponent means the number is multiplied by ten to that power, which can quickly result in a very large number.