Exercise: 3-G
Multiple Choice Type
Q1: The decimal 0.55 when expressed as a in the simplest form is
Solution:
0.55 can be written as \(\frac{55}{100}\).
Now, simplify \(\frac{55}{100}\). The GCD (Greatest Common Divisor) of 55 and 100 is 5.
Divide both the numerator and denominator by 5:
\[
\frac{55 \div 5}{100 \div 5} = \frac{11}{20}
\]
Thus, the simplest form is \(\frac{11}{20}\).
Answer: b. \(\frac{11}{20}\)
Q2: The fraction \(31\frac{3}{8}\) converted to decimal is
Solution:
Convert the mixed fraction to an improper fraction:
\[
31\frac{3}{8} = \frac{(31 \times 8) + 3}{8} = \frac{248 + 3}{8} = \frac{251}{8}
\]
Now divide 251 by 8:
\[
251 \div 8 = 31.375
\]
Thus, \(31\frac{3}{8}\) as a decimal is 31.375.
Answer: c. 31.375
Q3: What is subtracted 5.1 to get 0.51?
Solution:
We need to find the difference: \(5.1 – 0.51\).
Subtract the numbers:
\[
5.1 – 0.51 = 4.59
\]
Thus, the number to subtract is 4.59.
Answer: c. 4.59
Q4: 92.008 × 100 is equal to
Solution:
When we multiply 92.008 by 100, we shift the decimal point two places to the right:
\[
92.008 \times 100 = 9200.8
\]
Thus, 92.008 × 100 = 9200.8
Answer: d. 9200.8
Q5: A batsman 574 runs in 8 innings. His average score per innings is
Solution:
To find the average score, we divide the total runs by the number of innings:
\[
\text{Average} = \frac{574}{8} = 71.75
\]
Thus, the average score is 71.75.
Answer: b. 71.75
Q6: The recurring decimal \(0.4\bar{5}\) when converted to a vulgar fraction is
Solution:
Let \( x = 0.\overline{45} \), which represents the recurring decimal.
Multiply both sides of the equation by 10 to move the decimal point:
\[
10x = 4.\overline{45}
\]
Now subtract the first equation from this:
\[
10x – x = 4.\overline{45} – 0.\overline{45}
\]
\[
9x = 4
\]
Solve for \(x\):
\[
x = \frac{4}{9}
\]
Thus, the recurring decimal \(0.\overline{45}\) as a fraction is \(\frac{4}{9}\).
Answer: c. \(\frac{41}{99}\)
Q7: The decimal 371.6258 rounded off correct to two decimal places is
Solution:
To round 371.6258 to two decimal places, observe the third decimal place (5). Since it’s 5 or greater, we round up the second decimal place from 2 to 3:
\[
371.6258 \approx 371.63
\]
Thus, 371.6258 rounded to two decimal places is 371.63.
Answer: b. 371.63
