Using a number line, what whole number and rational number to the nearest half is 58−−√ between?
Responses
between 8.5 and 9
between 8.5 and 9
between 7 and 7.5
between 7 and 7.5
between 7.5 and 8
between 7.5 and 8
between 8 and 8.5
between 8 and 8.5
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: √81 –√88
The inequality is: √81 < √88
Write 6,739 in expanded form.(1 point)
Responses
(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)+(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
(6×1,000)+(7×100)+(3×10)+(0×1)
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 0 times 1 right parenthesis
(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
811 as a repeating decimal is 811.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we can perform long division:
72
___________
11 | 8.000
7 7
________
300
286
________
140
132
________
80
77
________
30
22
________
80
The remainder is 80. This means that the decimal representation of 8/11 is approximately 0.727272... The digits 72 repeat indefinitely, so we can write it as 0.72¯¯¯.