System of units Factors and Fraction
Workshop Calculation and Science, Module-1
Q1: What are the two classifications of system of units?
- British and Metric
- Gravitational and non-gravitational
- Fundamental and derived
- Metric and International
Q2: What are fundamental units?
- Length, Mass, Volume
- Length, Mass, Time
- Length, Mass, Area
- Length, Pressure, Volume
Q3: What denotes letter 'M' in MKS system?
- Mile
- Meter
- Millimeter
- Micron
Q4: How many millimetres are there in 1 inch?
- 2.54 mm
- 25.4 mm
- 24.5 mm
- 2.45 mm
Q5: What is the LCM of 12, 18, 6, 36?
- 12
- 18
- 36
- 42
Show Calculation
\[ \begin{array}{r|cccc} \color{red}2 & 12, & 18, & 6, & 36 \\ \hline \color{red}2 & 6, & 9, & 3, & 18 \\ \hline \color{red}3 & 3, & 9, & 3, & 9 \\ \hline \color{red}3 & 1, & 3, & 1, & 3 \\ \hline & 1, & 1, & 1, & 1 \\ \end{array} \quad \]
\[ \text{LCM} = 2 \times 2 \times 3 \times 3 = 36 \]
Q6: What is the HCF of 18, 42, 24?
- 2
- 6
- 18
- 24
Show Calculation
\[ \begin{array}{r|ccc} \color{red}2 & 18, & 42, & 24 \\ \hline \color{red}3 & 9, & 21, & 12 \\ \hline & 3, & 7, & 4 \\ \end{array} \quad \]
\[ \text{HCF} = 2 \times 3 = 6 \]
Q7: What is the improper fraction for the given mixed fraction \(7 \dfrac{3}{7}\)?
- 20/5
- 5/2
- 4/3
- 52/7
Show Calculation
To convert a mixed fraction to an improper fraction:
\( 7 \dfrac{3}{7} = \dfrac{7 \times 7 + 3}{7} = \dfrac{49 + 3}{7} = \dfrac{52}{7} \)
Q8: Convert decimal 0.000659 to fraction?
- 659/1000
- 659/10000
- 659/100000
- 659/1000000
Show Calculation
0.000659 has 6 decimal places:
\(0.000659 = \dfrac{659}{10^6} = \dfrac{659}{1000000}\)
Q9: Simplify: \(\frac{3}{4} + \frac{2}{5} - \frac{5}{20}\)
- \(\frac{9}{10}\)
- \(\frac{13}{10}\)
- \(\frac{23}{20}\)
- \(\frac{25}{20}\)
Show Calculation
Convert all terms to have denominator 20:
\[ \frac{3}{4} = \frac{15}{20},\quad \frac{2}{5} = \frac{8}{20},\quad \frac{5}{20} = \frac{5}{20} \]
Now compute:
\[ \frac{15 + 8 - 5}{20} = \frac{18}{20} = \frac{\cancel{18}^{^{9}}}{\cancel{20}^{^{10}}} = \frac{9}{10} \]
Q10: Divide: \(\frac{20}{31} \div \frac{15}{62}\)
- \(2 \frac{4}{3}\)
- \(2 \frac{1}{3}\)
- \(2 \frac{3}{2}\)
- \(2 \frac{2}{3}\)
Show Calculation
\( \frac{20}{31} \div \frac{15}{62} = \frac{\cancel{20}^{^{4}}}{\cancel{31}} \times \frac{\cancel{62}^{^{2}}}{\cancel{15}^{^{3}}} = \frac{8}{3} \)
Convert to mixed number:
\( \frac{8}{3} = 2 \frac{2}{3} \)
Q11: What is the product of 0.003 x 0.5?
- 0.00015
- 0.0015
- 0.015
- 0.15
Show Calculation
\( 0.003 \times 0.5 = \dfrac{3}{1000} \times \dfrac{5}{10} \)
= \(\dfrac{15}{10000} = 0.0015 \)
Q12: Simplify: \(\frac{17.49 \times 5.2}{6.5}\)
- 13.69
- 13.79
- 13.89
- 13.99
Show Calculation
Step 1: Multiply the numerator:
\[ 17.49 \times 5.2 = 90.948 \]
Step 2: Divide by 6.5:
\[ \frac{90.948}{6.5} = 13.992 \approx 13.99 \]
Final Answer: \(\boxed{13.99}\)
Q13: What is the length of each part if a copper wire of 225 metre is cut into 900 equal parts?
- 0.23 metre
- 0.25 metre
- 0.28 metre
- 0.29 metre
Show Calculation
\[ \text{Length of each part} = \dfrac{225}{900} = 0.25\ \text{metres} \]