How to Convert Decimals Expansions

Multiply by $100$ to get $ \frac{25}{100} $, and simplify to $ \frac{1}{4} $.

Multiply by $1000$ to get $ \frac{125}{1000} $, which simplifies to $ \frac{1}{8} $.

Multiply by $100$ to obtain $ \frac{75}{100} $, which simplifies to $ \frac{3}{4} $.

Let $ x = 0.777... $, $ 10x = 7.777... $, $ 9x = 7 $, so $ x = \frac{7}{9} $.

Let $ x = 0.8181... $, $ 100x = 81.8181... $, $ 99x = 81 $, so $ x = \frac{81}{99} = \frac{9}{11} $.

Let $ x = 0.2121... $, $ 100x = 21.2121... $, $ 99x = 21 $, so $ x = \frac{21}{99} = \frac{7}{33} $.

Multiply by 100 to get 65%, so $ 0.65 = 65% $.

Multiply by 100 to get 3%, so $ 0.03 = 3% $.

Multiply by 100 to get 250%, so $ 2.5 = 250% $.

Move the decimal to get 7.3, moved 3 places to the left, so $ 7.3 \times 10^{-3} $.

Move the decimal to get 1.2, moved 6 places to the left, so $ 1.2 \times 10^{-6} $.

Move the decimal to get 9, moved 2 places to the left, so $ 9 \times 10^{-2} $.

Divide 15 by 2 until the quotient is 0: The binary is 1111.

Divide 7 by 16 (quotient is 0, remainder 7): The hexadecimal is 7.

Divide 10 by 8 to get 1 remainder 2: The octal is 12.

Multiply the decimal by 10ⁿ, where n is the number of decimal places, to move the decimal point, then simplify the resulting fraction.

Yes, repeating decimals can be converted into fractions by setting up an equation with the repeating decimal as an unknown and solving for it.

Multiply the decimal by 100 and attach the percent sign (%) to convert it into a percentage.

Move the decimal point to create a new number between 1 and 10, then multiply by 10 raised to the number of places the decimal was moved, using a negative exponent if the original number was less than 1.

To convert decimals to binary, divide the number by 2 and record the remainder. Continue dividing and recording remainders until the quotient is 0. Read the binary number as the remainders in reverse order of the divisions.

Yes, the process is similar, but binary is base 2 and hexadecimal is base 16. For hexadecimal, you divide by 16 instead of 2 and use hexadecimal digits (0-9 and A-F).

Convert a decimal to an octal number by dividing the number by 8 and repeatedly recording the remainders until the quotient is 0, then read the remainders in reverse order.

Yes, all decimals can be converted into fractions. Non-repeating decimals become finite fractions, and repeating decimals become fractions with repeating numerators.

Move the decimal to the right of the first non-zero digit to form a number between 1 and 10, then multiply by 10 to the power of the negative of the number of places moved.

Multiplying by 100 shifts the decimal place two positions to the right, converting it to a percentage form, which is essentially the number per hundred.