When rounding a number to the nearest 100 , which place value column determines how it rounds? E.g. round 14, 578 to the nearest 100

When rounding a number to the nearest 100 , the digit in the tens place value column determines how the number rounds. E.g. when rounding 14, 578 to the nearest 100, the 7 in the tens column tells you to round up to 14, 600

How do you find the first significant figure of a number?

The first significant figure of a number is the first non-zero digit of the number when reading from left to right. For example, the first significant figure of 0.457 is 4.

True or False? The second significant figure of 4.0051 is 5.

False. The second significant figure of 4.0051 is 0 . The number 0 can be a significant figure as long as there are non-zero values on either side of it.

How do you round a number to three significant figures ? E.g. round 40, 529 to 3 s.f.

To round a number to three significant figures : Find the third significant figure Check the digit to its right (the fourth significant figure) If this is 0, 1, 2, 3 or 4 then keep the third significant figure the same and (if necessary) fill the remaining place values with 0s If it is 5, 6, 7, 8 or 9 then round the third significant figure up to the next value and (if necessary) fill the remaining place values with 0s E.g. the fourth significant figure of 40 529 is 2, this means the third significant figure (5) stays the same and it rounds down to 40 500.

Truncation is essentially the same as rounding down to a given degree of accuracy. You can think of it as "chopping off" the last parts of a number. For example if the question is about the maximum number of people that can fit in a taxi and the answer is 4.6, the answer would be truncated to 4, rather than rounded to 5.

True or False? Truncating a number to 3 decimal places will always produce the same result as rounding a number to 3 decimal places.

False. Truncating a number to 3 decimal places will often produce a different result to rounding a number to 3 decimal places. E.g. Rounding 3.57867 to 3 decimal places would be 3.579 Truncating 3.57867 to 3 decimal places would be 3.578

If you round both numbers up when estimating an addition , will the answer be an overestimate or an underestimate ?

If you round both numbers up in an addition, the answer will be an overestimate . E.g. estimate the calculation 288 + 962. Each value rounds up to 1 significant figure, 300 + 1000 = 1300. (This gives an overestimate 288 + 962 = 1250).

If you round both numbers down when estimating a multiplication , will the answer be an overestimate or an underestimate ?

If you round both numbers down in a multiplication, the answer will be an underestimate . E.g. estimate the calculation 621 × 438. Each value rounds down to 1 significant figure, 600 × 400 = 240 000. (This gives an underestimate 621 × 438 = 271 998.)

True or False? If you round both numbers up when estimating a division , the answer will be an overestimate .

False. If you round both numbers up when estimating a division , it is not easy to tell whether the the answer be an overestimate or an underestimate .

True or False? When estimating a subtraction, a - b , if a is rounded up and b is rounded down , the result will be an underestimate .

False. When estimating a subtraction, a - b , if a is rounded up and b is rounded down , the result will be an overestimate . E.g. estimate the calculation 487 - 317. Rounding each value to 1 significant figure, 500 - 300 = 200. (This gives an overestimate 487 -317 = 170).

Define the term lower bound .

The lower bound refers to the smallest value that a rounded number could be.

What is an error interval ?

An error interval is the range of values that a rounded number could be.

True or False? When a number is rounded to one decimal place , the answer is 4.8 . The upper bound for this number is 4.85 .

True. When a number is rounded to one decimal place , the answer is 4.8 . The upper bound for this number is 4.85 .

A number has been rounded to the nearest 10 , e.g. 780. How do you find the lower and upper bounds for the number?

A number has been rounded to the nearest 10 . Halve 10 to get 5. Add 5 to the rounded number to get the upper bound. Subtract 5 from the rounded number to get the lower bound. E.g. 780 has been rounded to the nearest 10. 10 ÷ 2 = 5 Upper bound: 780 + 5 = 785 Lower bound: 780 - 5 = 775

How do you find bounds when a number has been truncated ?

To find the bounds when truncating : Remember that truncating a number means to round it down . This means that the UPPER BOUND is found by adding 1 to the digit in the place value that the number was truncated to. The LOWER BOUND is always the number the value was truncated to. For example, the error interval for the number 1230, which has been truncated to 3 significant figures, is 1230 ≤ x < 1240.

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FrontRounding & Estimation
When rounding a number to the nearest 100, which place value column determines how it rounds?
E.g. round 14, 578 to the nearest 100

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Cards in this collection (23)

When rounding a number to the nearest 100, which place value column determines how it rounds?
E.g. round 14, 578 to the nearest 100
When rounding a number to the nearest 100, the digit in the tens place value column determines how the number rounds.
E.g. when rounding 14, 578 to the nearest 100, the 7 in the tens column tells you to round up to 14, 600
How do you find the first significant figure of a number?
The first significant figure of a number is the first non-zero digit of the number when reading from left to right.
For example, the first significant figure of 0.457 is 4.
True or False?
The second significant figure of 4.0051 is 5.
False.
The second significant figure of 4.0051 is 0.
The number 0 can be a significant figure as long as there are non-zero values on either side of it.
How do you round a number to three significant figures?
E.g. round 40, 529 to 3 s.f.
To round a number to three significant figures:
1. Find the third significant figure
2. Check the digit to its right (the fourth significant figure)
  If this is 0, 1, 2, 3 or 4 then keep the third significant figure the same and (if necessary) fill the remaining place values with 0s
  If it is 5, 6, 7, 8 or 9 then round the third significant figure up to the next value and (if necessary) fill the remaining place values with 0s
E.g. the fourth significant figure of 40 529 is 2, this means the third significant figure (5) stays the same and it rounds down to 40 500.
What is the general rule for rounding when performing estimating a calculation?
E.g. estimate the calculation $\frac{2.1 \times 3.7}{0.9}$
When estimating a calculation, the general rule is to round each number to 1 significant figure first.
E.g. for the calculation $\frac{2.1 \times 3.7}{0.9}$ , round to $\frac{2 \times 4}{1} = 8$
What is truncation?
Truncation is essentially the same as rounding down to a given degree of accuracy. You can think of it as "chopping off" the last parts of a number.
For example if the question is about the maximum number of people that can fit in a taxi and the answer is 4.6, the answer would be truncated to 4, rather than rounded to 5.
True or False?
Truncating a number to 3 decimal places will always produce the same result as rounding a number to 3 decimal places.
False.
Truncating a number to 3 decimal places will often produce a different result to rounding a number to 3 decimal places.
E.g.
Rounding 3.57867 to 3 decimal places would be 3.579
Truncating 3.57867 to 3 decimal places would be 3.578
If you round both numbers up when estimating an addition, will the answer be an overestimate or an underestimate?
If you round both numbers up in an addition, the answer will be an overestimate.
E.g. estimate the calculation 288 + 962.
Each value rounds up to 1 significant figure, 300 + 1000 = 1300.
(This gives an overestimate 288 + 962 = 1250).
If you round both numbers down when estimating a multiplication, will the answer be an overestimate or an underestimate?
If you round both numbers down in a multiplication, the answer will be an underestimate.
E.g. estimate the calculation 621 × 438.
Each value rounds down to 1 significant figure, 600 × 400 = 240 000.
(This gives an underestimate 621 × 438 = 271 998.)
True or False?
If you round both numbers up when estimating a division, the answer will be an overestimate.
False.
If you round both numbers up when estimating a division, it is not easy to tell whether the the answer be an overestimate or an underestimate.
True or False?
When estimating a subtraction, a - b, if a is rounded up and b is rounded down, the result will be an underestimate.
False.
When estimating a subtraction, a - b, if a is rounded up and b is rounded down, the result will be an overestimate.
E.g. estimate the calculation 487 - 317.
Rounding each value to 1 significant figure, 500 - 300 = 200.
(This gives an overestimate 487 -317 = 170).
Define the term lower bound.
The lower bound refers to the smallest value that a rounded number could be.
What is an error interval?
An error interval is the range of values that a rounded number could be.
True or False?
If $x$ is a rounded number, the error interval for $x$ can be written as $lower bound \leq x \leq upper bound$ .
False.
If $x$ is a rounded number, the error interval for $x$ can not be written as $lower bound \leq x \leq upper bound$ because $x$ can not be equal to the upper bound.
Instead, $lower bound \leq x < upper bound$ is the correct statement.
True or False?
When a number is rounded to one decimal place, the answer is 4.8.
The upper bound for this number is 4.85.
True.
When a number is rounded to one decimal place, the answer is 4.8.
The upper bound for this number is 4.85.
A number has been rounded to the nearest 10, e.g. 780.
How do you find the lower and upper bounds for the number?
A number has been rounded to the nearest 10.
Halve 10 to get 5.
Add 5 to the rounded number to get the upper bound.
Subtract 5 from the rounded number to get the lower bound.
E.g. 780 has been rounded to the nearest 10.
10 ÷ 2 = 5
Upper bound: 780 + 5 = 785
Lower bound: 780 - 5 = 775
What do you need to do to the lower and upper bounds of $x$ to find the lower and upper bounds of $4 x$ ?
To find the lower and upper bounds of $4 x$ , you need to:
- Multiply the lower bound of $x$ by $4$ to find the lower bound of $4 x$ .
- Multiply the upper bound of $x$ by $4$ to find the upper bound of $4 x$ .
Which bounds for $a$ and $b$ should you use to find the lower bound of $a + b$ ?
To find the lower bound of $a + b$ , you should use the lower bounds of $a$ and $b$ .
Which bounds for $a$ and $b$ should you use to find the upper bound of $a - b$ ?
To find the upper bound of $a - b$ , you should use the upper bound of $a$ and the lower bound of $b$ .
True or False?
To find the upper bound of $\frac{a}{b}$ , you should use the upper bound of $a$ and the upper bound of $b$ .
False.
To find the upper bound of $\frac{a}{b}$ , you should use the upper bound of $a$ and the lower bound of $b$ .
True or False?
To find the lower bound of $a b$ , you should use the lower bound of $a$ and the lower bound of $b$ .
True.
To find the lower bound of $a b$ , you should use the lower bound of $a$ and the lower bound of $b$ .
The upper bound of $x$ is 3.142345.
The lower bound of $x$ is 3.141871.
What level of accuracy should you use to round $x$ to?
Round $x$ to 4 significant figures (3.142) because both the upper and lower bounds agree as far as 4 significant figures.
How do you find bounds when a number has been truncated?
To find the bounds when truncating:
Remember that truncating a number means to round it down.
This means that the UPPER BOUND is found by adding 1 to the digit in the place value that the number was truncated to.
The LOWER BOUND is always the number the value was truncated to.
For example, the error interval for the number 1230, which has been truncated to 3 significant figures, is 1230 ≤ x < 1240.

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