A number in scientific notation has the format 0.000 x 10^exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:

638,000 in scientific notation is 6.38 x 10⁵

The equation for this sequence is:

a_n = a_n-1 + 2(n - 1)

where n is the term's order in the sequence, a_n is the value of the term, and a_n-1 is the value of the term before a_n. This makes the next number:

a₆ = a₅ + 2(6 - 1)
a₆ = 21 + 2(5)
a₆ = 31

To subtract these radicals together their radicands must be the same:

7\( \sqrt{18} \) - 6\( \sqrt{2} \)
7\( \sqrt{9 \times 2} \) - 6\( \sqrt{2} \)
7\( \sqrt{3^2 \times 2} \) - 6\( \sqrt{2} \)
(7)(3)\( \sqrt{2} \) - 6\( \sqrt{2} \)
21\( \sqrt{2} \) - 6\( \sqrt{2} \)

Now that the radicands are identical, you can subtract them:

Average speed in miles per hour is the number of miles traveled divided by the number of hours:

Solving for distance:

distance = \( \text{speed} \times \text{time} \)
distance = \( 20mph \times 7h \)
140 miles

A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.