9 Questions
How is the number 0.2353535... expressed in the form p/q?
0.233
What is the result when multiplying x by 100 as shown in the text?
23.5
What is the value of x when 99x equals 23.3 in the text?
0.235
Which of the following statements is true about rational numbers based on the text?
Rational numbers can have either terminating or non-terminating recurring decimal expansions.
What can be concluded about the decimal expansions of irrational numbers from the text?
They are always non-terminating non-recurring.
In the context of rational numbers, what is meant by a 'non-terminating recurring' decimal expansion?
A decimal that repeats a pattern of digits indefinitely.
How is the number 0.3333... expressed in the form p/q according to the text?
$1/3$
What is the significance of multiplying a number by 100 to convert a repeating decimal to an equation as shown in the text?
It helps remove the repeating decimals.
'Every number with a non-terminating recurring decimal expansion can be expressed in which form according to the text?'
$p/q$ where $p$ and $q$ are integers and $q \neq 0$
Explore the patterns that emerge when dividing rational numbers of the form p/q, where q is not equal to zero. Understand the scenarios where the remainder becomes zero or forms a repeating string of remainders. Analyze each case with detailed examples.
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