problem archive
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Given \( \sin(A) = \frac{3}{5} \) and \( \sin(B) = \frac{5}{13} \), find \( \sin(A + B) \) -
Are the following statements true or false? Give reasons for your answers. (i) Every whole number is a natural number. (ii) Every integer is a rationa... -
Find five rational numbers between 1 and 2. -
Is zero a rational number? Can you write it in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \)? -
Find six rational numbers between 3 and 4. -
Find five rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \). -
State whether the following statements are true or false. Give reasons for your answers. (i) Every natural number is a whole number. (ii) Every intege... -
Locate \( \sqrt{2} \) on the number line. -
Locate \( \sqrt{3} \) on the number line. -
State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number. (ii) Every point on the ... -
Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number. -
Show how \(\sqrt{5}\) can be represented on the number line. -
Find the decimal expansions of \( \frac{10}{3} \), \( \frac{7}{8} \), and \( \frac{1}{7} \) -
Show that 3.142678 is a rational number. In other words, express 3.142678 in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \(... -
Show that 0.3333... = \( 0.\overline{3} \) can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). -
Show that 1.272727... = 1.27 can be expressed in the form \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \neq 0 \). -
Show that 0.2353535... = 0.2\overline{35} can be expressed in the form \frac{p}{q}, where p and q are integers and q \neq 0. -
Find an irrational number between \( \frac{1}{7} \) and \( \frac{2}{7} \) -
Write the following in decimal form and say what kind of decimal expansion each has: (i) \( \frac{36}{100} \) (ii) \( \frac{1}{11} \) (iii) \( \frac{4... -
You know that \( \frac{1}{7} = 0.142857 \). Can you predict what the decimal expansions of \( \frac{2}{7} \), \( \frac{3}{7} \), \( \frac{4}{7} \), \(...