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Write the following four numbers in order, from the smallest to the biggest - Junior Cycle Mathematics - Question 6 - 2016
Question 6
Write the following four numbers in order, from the smallest to the biggest. 22/7 π √10 3.14 Put a tick (✓) in the correct box in each row of the table below to sh... show full transcript
Worked Solution & Example Answer:Write the following four numbers in order, from the smallest to the biggest - Junior Cycle Mathematics - Question 6 - 2016
Step 1
Write the following four numbers in order, from the smallest to the biggest.
Answer
To order the numbers, we first approximate the values:
- (a rational number)
- (an irrational number)
- (an irrational number)
- (exact value)
Arranging these from smallest to largest:
- 3.14
Thus, the order is: 3.14, π, rac{22}{7}, √10.
Step 2
Put a tick (✓) in the correct box in each row of the table below to show whether each number is rational or irrational. Give a reason for each answer.
Answer
| Number | Rational | Irrational | Reason |
|---|---|---|---|
| √10 | ✓ | It cannot be written as a fraction using only integers or it goes on forever without repeating as a decimal. | |
| 3.14 | ✓ | It can be written as a fraction using only integers (e.g. ( \frac{314}{100} )). |
Step 3
How many digits does the number 3.14 × 10^100 have, when it is written out fully?
Answer
To find the number of digits in 3.14 × 10^100, consider the following:
- The number 3.14 has 3 digits.
- The multiplication by 10^100 means we add 100 zeros to the end of 3.14.
Thus, the total number of digits is:
- 3 (from 3.14) + 100 (from 10^100) = 103 digits.
Therefore, the answer is:
Answer: 103
Justification: The number 3.14 has 2 digits before the decimal and the result of 3.14 × 10^100 would have 100 additional digits, resulting in 103 digits in total.