Decimals & Fractions: Level 1

Solution (C): To convert a fraction to a decimal, divide the numerator by the denominator. \(3 \div 4 = 0.75\).

Solution (A): \(0.5\) is read as “five tenths”, which is written as \( \frac{5}{10} \). This fraction simplifies to \( \frac{1}{2} \).

Solution (D): To round to the nearest tenth, we look at the digit in the hundredths place (4). Since 4 is less than 5, we round down. *Correction:* The digit in the hundredths place is 4, but the digit in the thousandths place is 5. Let’s re-read the question. “12.345 to the nearest tenth”. We look at the tenths digit (3). The digit to its right is 4. Since 4 is less than 5, we round down. The answer should be 12.3 (C).

Solution (C): To round to the nearest tenth, we look at the digit in the tenths place (3). The digit immediately to its right is 4. Since 4 is less than 5, we “round down” (i.e., keep the tenths digit as is). The result is 12.3.

Solution (B): To round to the nearest inch as 8, the original number must be in the range [7.5, 8.5). (A) 7.4 is too small. (B) 7.5 is in the range (it rounds up to 8). (C) 8.5 is not in the range (it would round up to 9). (D) 8.6 is too large. (E) 7.49 is too small.

Solution (A): The repeating pattern is “123”, which has a length of 3 digits. We divide 100 by 3: \(100 \div 3 = 33\) with a remainder of 1. A remainder of 1 means it is the 1st digit in the pattern, which is 1.

Solution (C): To add fractions, we need a common denominator, which is 4. \( \frac{1}{2} \) is equal to \( \frac{2}{4} \). So, \( \frac{2}{4} + \frac{1}{4} = \frac{3}{4} \).

Solution (B): To compare decimals, we can add zeros to make them the same length. A) 0.190 B) 0.200 C) 0.099 D) 0.199 E) 0.100 Comparing the numbers, 200 is the largest. So, 0.2 is the largest.

Solution (C): To round to 1.5 (the nearest tenth), the original number must be in the range [1.45, 1.55). (A) 1.44 is too small. (B) 1.55 would round up to 1.6. (C) 1.48 is in the range. (D) 1.4 is too small. (E) 1.59 is too large.

Solution (D): The repeating pattern is “9876”, which has a length of 4 digits. We divide 20 by 4: \(20 \div 4 = 5\) with a remainder of 0. A remainder of 0 means the digit is the last one in the pattern (the 4th digit), which is 6.

Solution (A): To convert a fraction to a percentage, find the equivalent fraction out of 100. \( \frac{1}{5} = \frac{20}{100} \). This is equal to 20%.