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.