4 (a) Use one of these symbols <, > or = to make each statement true - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Question 4
4 (a) Use one of these symbols <, > or = to make each statement true.
(i) \( \frac{1}{4} \) .......... 0.25
(ii) 0.66 .......... \( \frac{2}{3} \)
(iii) 6 .......... show full transcript
Worked Solution & Example Answer:4 (a) Use one of these symbols <, > or = to make each statement true - OCR - GCSE Maths - Question 4 - 2017 - Paper 1
Step 1
(i) \( \frac{1}{4} \) .......... 0.25
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Answer
To determine the relationship between ( \frac{1}{4} ) and 0.25, we convert ( \frac{1}{4} ) into decimal form:
[ \frac{1}{4} = 0.25 ]
Thus, the correct symbol to use is:
[ \frac{1}{4} = 0.25 ]
Step 2
(ii) 0.66 .......... \( \frac{2}{3} \)
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Answer
Next, we need to compare 0.66 with ( \frac{2}{3} ). We convert ( \frac{2}{3} ) to decimal:
[ \frac{2}{3} \approx 0.6667 ]
Since 0.66 is less than ( 0.6667 ), the appropriate symbol is:
[ 0.66 < \frac{2}{3} ]
Step 3
(iii) 6 .......... \( 2^3 \)
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Answer
Now we compare 6 with ( 2^3 ):
[ 2^3 = 8 ]
Since 6 is less than 8, we use the symbol:
[ 6 < 2^3 ]
Step 4
(b) Write down the inequality for \( x \) that is shown on this number line.
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Answer
From the number line, it is observed that ( x ) is greater than 2 but less than or equal to 7. Therefore, the inequality is:
