What fraction and decimal, in the hundredths is equivalent to 7/100?
The Correct Answer and Explanation is :
The fraction ( \frac{7}{100} ) can be converted into both a decimal and a fraction equivalent in decimal form.
Fraction to Decimal:
The fraction ( \frac{7}{100} ) means that we are dividing 7 by 100. When we divide 7 by 100, we get:
[
7 \div 100 = 0.07
]
So, ( \frac{7}{100} ) as a decimal is 0.07.
Decimal Representation:
In decimal form, ( 0.07 ) represents 7 hundredths because the “7” is in the hundredths place, which is the second place to the right of the decimal point.
Why This Works:
The denominator of 100 means that the value of the fraction is based on the number of hundredths. The fraction ( \frac{7}{100} ) directly represents 7 parts of 100 equal parts, or 7 hundredths.
To understand the relationship more clearly, consider this: When you divide by 100, you are essentially moving the decimal point two places to the left in the number. If you start with the number 7 (which is equivalent to 7.00 in decimal form) and divide it by 100, the decimal point shifts two places to the left, giving you 0.07.
Fraction and Decimal Equivalence:
- Fraction: ( \frac{7}{100} )
- Decimal: ( 0.07 )
Thus, both ( \frac{7}{100} ) as a fraction and 0.07 as a decimal represent the same value. It’s also worth noting that this decimal representation is accurate to the hundredths place, as the number 0.07 ends after two decimal places, making it a precise representation of ( \frac{7}{100} ).