A total of 7,803,100 tourists visited Country A from the year 2018 to the year 2020. Round to the nearest place value, then express this number in the form of a single digit times an integer power of 10
To express 7,803,100 in the form of a single digit times an integer power of 10, we can round it to the nearest place value, which is the nearest million.
Rounding 7,803,100 to the nearest million, we get 8,000,000.
Expressing this number in scientific notation, we have:
8,000,000 = 8 * 10^6.
Therefore, 7,803,100 tourists can be expressed as 8 * 10^6.
Two weeks before an examination day, a librarian monitored the number of students who visited the library. Then they compared it with the number of visits made in an average week. Approximately 2×103
visits were reflected in their logbook during this two-week period, while only about 5×102
were reflected on an average week. How many times higher is the number of library visits before examination day compared to the library visits in an average week? Your answer should be a whole number.
To find out how many times higher the number of library visits before the examination day is compared to the number of visits in an average week, we need to divide the number of visits before the examination day by the number of visits in an average week.
The number of visits before the examination day is approximately 2x10^3, while the number of visits in an average week is approximately 5x10^2.
Dividing the number of visits before the examination day by the number of visits in an average week, we get:
(2x10^3) / (5x10^2)
= 2/5 * (10^3 / 10^2)
= 2/5 * 10^(3-2)
= 2/5 * 10^1
= 2 * 10/5
= 4
Therefore, the number of library visits before the examination day is 4 times higher compared to the number of visits in an average week.
It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a×10n
where a
is single digit.
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Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.
To convert 8/11 into a repeating decimal, divide 8 by 11. The result is 0.727272...
In this case, the digit 27 repeats indefinitely. Thus, we can express 8/11 as a repeating decimal by placing a bar over the repeating digits:
8/11 = 0.72¯¯¯.
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 will use the following method:
Let x = 0.72¯¯¯
We multiply both sides of the equation by 1000 (to move the decimal point three places to the right):
1000x = 727.272¯¯¯
Now, let's subtract the original equation from the new equation:
1000x - x = 727.272¯¯¯ - 0.72¯¯¯
Simplifying both sides:
999x = 726.552¯¯¯
To get rid of the repeating decimal, we can subtract the equation obtained by multiplying both sides by 1000. This eliminates the repeating part:
1000x - x = 727.272¯¯¯ - 0.72¯¯¯
Simplifying both sides:
999x = 726.552
Now, divide both sides of the equation by 999 to solve for x:
x = 726.552 / 999
Simplifying the expression by finding the greatest common divisor (GCD) of 726.552 and 999:
GCD(726.552, 999) = 3
Dividing both the numerator and denominator by 3:
x = (726.552 / 3) / (999 / 3)
x = 242.184 / 333
Further simplifying by dividing both the numerator and denominator by 3:
x = 80.728 / 111
Therefore, the rational number equivalent to 0.72¯¯¯ is 80.728/111 in simplest form.
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It takes 10 years for a $100 monthly bank deposit to amount to $15,528.23 when invested at 5% interest compounded monthly. Round to the nearest place value, then express the amount $15,528.23 in the form of a × 10^n
where "a" is single digit.
To express $15,528.23 in the form of a×10^n, we need to determine the value of a and n.
We know that the amount after 10 years is $15,528.23. Let's use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where A is the amount after t years, P is the principal amount (monthly deposit), r is the annual interest rate (5% or 0.05), n is the number of times interest is compounded per year (12), and t is the number of years.
In this case, we have:
A = $15,528.23
P = $100
r = 0.05
n = 12
t = 10
Using the formula and solving for A:
$15,528.23 = $100(1 + 0.05/12)^(12*10)
Dividing both sides by $100 and rearranging the equation:
155.2823 = (1 + 0.05/12)^(12*10)
Taking the natural logarithm of both sides to isolate the exponent:
ln(155.2823) = ln((1 + 0.05/12)^(12*10))
ln(155.2823) = (12*10) * ln(1 + 0.05/12)
Using a calculator, we find:
ln(155.2823) ≈ 5.049856
Simplifying the equation:
5.049856 = 120 * ln(1 + 0.05/12)
Dividing both sides by 120:
0.04208213 = ln(1 + 0.05/12)
Using the inverse natural logarithm to isolate (1 + 0.05/12):
1.0423863 ≈ 1 + 0.05/12
Subtracting 1 and multiplying by 12 to isolate 0.05:
0.0163583 ≈ 0.05
Therefore, the interest rate (0.05) is approximately 0.0163583 when rounded to the nearest place value.
Now, we can express the amount $15,528.23 in the form of a×10^n by moving the decimal point to the left until we have a single digit before the decimal point. In this case, we need to move the decimal point four places to the left to have 1.552823.
So,
$15,528.23 ≈ 1.552823 × 10^4
Therefore, the amount $15,528.23 can be expressed as 1.552823 × 10^4.