Final answer:
Hannah had 40% of her coins as 10-cent coins, which is also the decimal fraction 0.40. This is determined by the given ratio of two out of every five coins being 10-cent coins.
Step-by-step explanation:
If Hannah had some coins in her purse and two coins out of every five were 10-cent coins, we can calculate the percent and decimal fraction of the coins that were 10 cents.
Percent of 10-Cent Coins
A) To find what percent of Hannah's coins were 10-cent coins, we use the ratio of 10-cent coins to the total number of coins. As given, 2 out of every 5 coins are 10 cents, so we set up a fraction which is 2/5. To convert this to a percent, we multiply by 100:
(2/5) × 100 = 40%
Thus, 40% of Hannah's coins were 10-cent coins.
Decimal Fraction of 10-Cent Coins
B) To express this as a decimal fraction, we use the same fraction of 2/5:
2/5 = 0.40
Therefore, the decimal fraction of Hannah's coins that were 10 cents is 0.40.