Use one of the symbols , " data-type="inline-math"> or to make each statement true. .......... 0.2861 .......... 11% ..........

Goal: Use one of the symbols , " data-type="inline-math"> or to make each of the three given statements true.Step 1: Compare and .To compare the fraction with the decimal, we first convert the fraction to its decimal form by dividing 2 by 7.Now we compare this decimal value with . We can compare them digit by digit starting from the left.The digits in the tenths place are both 2.The digits in the hundredths place are both 8.The digit in the thousandths place for is 5, while for it is 6.Since , it follows that .Therefore, the correct symbol is .Step 2: Compare and .To compare these values, we should express them in the same format. Let's convert both to decimals.First, convert the percentage to a decimal: .Next, convert the fraction to a decimal. We can simplify the fraction first by dividing the numerator and the denominator by their greatest common divisor, which is 99, or simply by 9.As a decimal, .Since both expressions are equal to , they are equal to each other.Therefore, the correct symbol is .Step 3: Compare and .We evaluate each expression using the rules of exponents.Any number raised to the power of 3 is the number multiplied by itself three times:Any non-zero number raised to the power of 0 is equal to 1:Since both expressions evaluate to 1, they are equal.Therefore, the correct symbol is .Conclusion: The correct symbols to make the statements true are , , and respectively.

is a positive integer.Write these values in order of size, starting with the smallest.

Goal: Write the given values in order of size, starting with the smallest.Step 1: To compare the values, we convert each expression into a decimal multiple of . Since is a positive integer, the size of the expression is determined by its coefficient.The first value is .The second value is .The third value is .The fourth value is , which we calculate as:Step 2: We now compare the decimal coefficients: , , , and . Ordering these from smallest to largest gives the inequality . By matching the coefficients back to their original expressions, we can establish the final order.Conclusion: The values in order of size, starting with the smallest, are , , , .

Put a ring around each of the symbols that make this statement correct. \quad

To compare the two values, we must express them in the same format. Let's convert the percentage to a decimal.The percentage means 5 parts out of 100.Now we compare the decimal with the decimal .Since is greater than , the symbol " data-type="inline-math"> makes the statement correct: 5\%" data-type="inline-math">.Since is not equal to , the symbol also makes the statement correct: .The other symbols are incorrect: is false. is false.Therefore, the correct symbols to ring are and " data-type="inline-math">.

Write these values in order of size, starting with the smallest.

Goal: To write the given values in order of size, starting with the smallest.Step 1: Convert all the given values into a common decimal form to allow for easy comparison. is already in decimal form. We can write it as for easier comparison.. We know that and , so the value of is between and . A more precise value is approximately .Step 2: Now, we list the decimal values in ascending order.Step 3: Replace the decimal values with their original forms to present the final ordered list. The correct order is:Conclusion: The values in order of size from smallest to largest are .

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IGCSE (CAMBRIDGE)|9th and 10th|Extended Maths (0580)

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