Solved on Nov 13, 2023

Emma's number is between 825 and 875, inclusive. Find the smallest and largest possible values.

STEP 1

Assumptions1. Emma's number, when rounded to the nearest10, is850. . Emma's number, when rounded to1 significant figure, is800.
3. We are looking for whole numbers.

STEP 2

To understand the range of numbers that round to850 to the nearest10, we need to consider what rounding to the nearest10 means. A number will round to850 if it is halfway between840 and860.
$840 < Number <860$

STEP 3

Next, we need to understand the range of numbers that round to800 to1 significant figure. A number will round to800 if it is halfway between750 and850.
$750 < Number <850$

STEP 4

Now, we need to find the overlap of the two ranges. The smallest possible number Emma could be thinking of is the largest lower bound, and the largest possible number is the smallest upper bound.
$Max(840,750) < Number < Min(860,850)$

STEP 5

Calculate the maximum of the two lower bounds.
$Max(840,750) =840$

STEP 6

Calculate the minimum of the two upper bounds.
$Min(860,850) =850$

STEP 7

So, the smallest possible number Emma could be thinking of is840, and the largest possible number is850.
a) The smallest possible number Emma could be thinking of is840. b) The largest possible number Emma could be thinking of is850.

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Emma's number is between 825 and 875, inclusive. Find the smallest and largest possible values.

STEP 1

Assumptions1. Emma's number, when rounded to the nearest10, is850. . Emma's number, when rounded to1 significant figure, is800.
3. We are looking for whole numbers.

STEP 2

To understand the range of numbers that round to850 to the nearest10, we need to consider what rounding to the nearest10 means. A number will round to850 if it is halfway between840 and860.
$840 < Number <860$

STEP 3

Next, we need to understand the range of numbers that round to800 to1 significant figure. A number will round to800 if it is halfway between750 and850.
$750 < Number <850$

STEP 4

Now, we need to find the overlap of the two ranges. The smallest possible number Emma could be thinking of is the largest lower bound, and the largest possible number is the smallest upper bound.
$Max(840,750) < Number < Min(860,850)$

STEP 5

Calculate the maximum of the two lower bounds.
$Max(840,750) =840$

STEP 6

Calculate the minimum of the two upper bounds.
$Min(860,850) =850$

STEP 7

So, the smallest possible number Emma could be thinking of is840, and the largest possible number is850.
a) The smallest possible number Emma could be thinking of is840. b) The largest possible number Emma could be thinking of is850.

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Emma's number is between 825 and 875, inclusive. Find the smallest and largest possible values.

STEP 1

Assumptions1. Emma's number, when rounded to the nearest10, is850. . Emma's number, when rounded to1 significant figure, is800.3. We are looking for whole numbers.

STEP 2

To understand the range of numbers that round to850 to the nearest10, we need to consider what rounding to the nearest10 means. A number will round to850 if it is halfway between840 and860.840<Number<860840 < Number <860840<Number<860

STEP 3

Next, we need to understand the range of numbers that round to800 to1 significant figure. A number will round to800 if it is halfway between750 and850.750<Number<850750 < Number <850750<Number<850

STEP 4

Now, we need to find the overlap of the two ranges. The smallest possible number Emma could be thinking of is the largest lower bound, and the largest possible number is the smallest upper bound.Max(840,750)<Number<Min(860,850)Max(840,750) < Number < Min(860,850)Max(840,750)<Number<Min(860,850)

STEP 5

Calculate the maximum of the two lower bounds.Max(840,750)=840Max(840,750) =840Max(840,750)=840

STEP 6

Calculate the minimum of the two upper bounds.Min(860,850)=850Min(860,850) =850Min(860,850)=850

STEP 7

So, the smallest possible number Emma could be thinking of is840, and the largest possible number is850.a) The smallest possible number Emma could be thinking of is840. b) The largest possible number Emma could be thinking of is850.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Assumptions1. Emma's number, when rounded to the nearest10, is850. . Emma's number, when rounded to1 significant figure, is800.
3. We are looking for whole numbers.

To understand the range of numbers that round to850 to the nearest10, we need to consider what rounding to the nearest10 means. A number will round to850 if it is halfway between840 and860.
$840 < Number <860$

Next, we need to understand the range of numbers that round to800 to1 significant figure. A number will round to800 if it is halfway between750 and850.
$750 < Number <850$

Now, we need to find the overlap of the two ranges. The smallest possible number Emma could be thinking of is the largest lower bound, and the largest possible number is the smallest upper bound.
$Max(840,750) < Number < Min(860,850)$

Calculate the maximum of the two lower bounds.
$Max(840,750) =840$

Calculate the minimum of the two upper bounds.
$Min(860,850) =850$

So, the smallest possible number Emma could be thinking of is840, and the largest possible number is850.
a) The smallest possible number Emma could be thinking of is840. b) The largest possible number Emma could be thinking of is850.