Monique measured the widths of several stamps in her collection of world stamps. The measurements are 158in., 11116in., 134in., and 112in. What is the width of the widest stamp?
The widest stamp has a width of 158in.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.(1 point)
Responses
14.2 miles
14.2 miles
63.59 miles
63.59 miles
14.13 miles
14.13 miles
7.07 miles
The circumference of a circle with a diameter of 4.5 miles is approximately 14.13 miles.
Write 6,739 in expanded form.(1 point)
Responses
(6×1,000)+(7×100)+(3×10)+(9×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(7×100)+(3×10)+(9×1)
left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(0×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 811 as a repeating decimal, we divide 811 by the number 9 (since 9 is the largest single-digit number) and mark the cycle of repeating digits with a bar:
811 ÷ 9 = 90 remainder 1
So, the repeating decimal representation of 811 is 90.1 (where the digit 1 repeats indefinitely).
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can use algebraic manipulation.
Let x = 0.72¯¯¯¯¯.
Multiply both sides of the equation by 100 (to move the decimal point two places to the right):
100x = 72.72¯¯¯¯¯.
Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Divide both sides of the equation by 99 to solve for x:
x = 72/99
We can simplify the fraction 72/99 by dividing both the numerator and denominator by their greatest common divisor, which is 9:
x = 8/11
Therefore, the rational number equivalent of 0.72¯¯¯¯¯ is 8/11 in simplest form.
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 1 and 5/8 in, 1 and 11/16 in, 1 and 3/4 in, 1 and 1/2 in. What is the width of the widest stamp?
To find the width of the widest stamp, we need to compare the given measurements and determine which one is the largest.
The given measurements are:
1 and 5/8 in
1 and 11/16 in
1 and 3/4 in
1 and 1/2 in
To compare the measurements, we need to convert them to a common denominator. The common denominator should be a multiple of 16 (since 16 is the largest denominator among the given fractions).
Converting the measurements to a common denominator of 16:
1 and 5/8 in = 1 and 10/16 in
1 and 11/16 in stays the same
1 and 3/4 in = 1 and 12/16 in
1 and 1/2 in = 1 and 8/16 in
Now we can compare the measurements:
1 and 10/16 in
1 and 11/16 in
1 and 12/16 in
1 and 8/16 in
After comparing, we can see that the width of the widest stamp is 1 and 12/16 inches, which is equivalent to 1 and 3/4 inches.
Therefore, the width of the widest stamp is 1 and 3/4 inches.
ok thank you so much
You're welcome! If you have any more questions, feel free to ask.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
The relationship between rational numbers and whole numbers is that all whole numbers are rational numbers, but not all rational numbers are whole numbers.
A rational number is defined as any number that can be expressed as a ratio of two integers, where the denominator is not zero. This includes whole numbers since they can be expressed as the ratio of an integer over 1. For example, the whole number 5 can be written as the rational number 5/1.
On the other hand, not all rational numbers are whole numbers. Rational numbers include fractions (proper or improper), mixed numbers, and repeating or terminating decimals. For example, the rational number 3/2 is a fraction that is not a whole number, and the rational number 2.75 is a decimal that is also not a whole number.
To summarize:
- All whole numbers are rational numbers.
- Not all rational numbers are whole numbers.