If the tiger has consumed 90 pounds of food in 10 days that's \( \frac{90}{10} \) = 9 pounds of food per day. The tiger needs to consume 117 - 90 = 27 more pounds of food to reach 117 pounds total. At 9 pounds of food per day that's \( \frac{27}{9} \) = 3 more days.

To multiply fractions, multiply the numerators together and then multiply the denominators together:

\( \frac{2}{6} \) x \( \frac{2}{7} \) = \( \frac{2 x 2}{6 x 7} \) = \( \frac{4}{42} \) = \(\frac{2}{21}\)

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{3!}{2!} \)
\( \frac{3 \times 2 \times 1}{2 \times 1} \)
\( \frac{3}{1} \)
3

To simplify this fraction, first find the greatest common factor between them. The factors of 16 are [1, 2, 4, 8, 16] and the factors of 76 are [1, 2, 4, 19, 38, 76]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{16}{76} \) = \( \frac{\frac{16}{4}}{\frac{76}{4}} \) = \( \frac{4}{19} \)

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:

7,714,000 in scientific notation is 7.714 x 10⁶