How can any decimal be represented?

How can any decimal be represented?

• A. As a simple fraction only
• B. As a fraction where the denominator is a power of ten
• C. As a mixed number
• D. As a percentage

Answer: (B)

Any decimal can be expressed as a fraction where the denominator is a power of ten because decimals are inherently linked to the base-10 number system. When a decimal is written, the position of each digit after the decimal point indicates a fraction of ten: for example, in the decimal 0.75, the 7 is in the tenths place (which is 7/10) and the 5 is in the hundredths place (which is 5/100). Therefore, 0.75 can be rewritten as 75/100, which simplifies to 3/4, illustrating its representation as a fraction ultimately derived from powers of ten. This concept is foundational in understanding fractions and decimals, as decimals represent numbers in increments of ten, making it straightforward to convert them into fractions with a denominator of a power of ten. Such a representation also allows for easy manipulation and understanding of the value of the decimal in relation to whole numbers and other fractions.

Any decimal can be expressed as a fraction where the denominator is a power of ten because decimals are inherently linked to the base-10 number system. When a decimal is written, the position of each digit after the decimal point indicates a fraction of ten: for example, in the decimal 0.75, the 7 is in the tenths place (which is 7/10) and the 5 is in the hundredths place (which is 5/100). Therefore, 0.75 can be rewritten as 75/100, which simplifies to 3/4, illustrating its representation as a fraction ultimately derived from powers of ten.

This concept is foundational in understanding fractions and decimals, as decimals represent numbers in increments of ten, making it straightforward to convert them into fractions with a denominator of a power of ten. Such a representation also allows for easy manipulation and understanding of the value of the decimal in relation to whole numbers and other fractions.