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.(1 point)
To find the amount in the form of a×10^n, we need to round $15,528.23 to the nearest place value and determine the value of a and n.
After 10 years of monthly $100 deposits at a 5% interest compounded monthly, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment
P = the principal amount (monthly deposit)
r = annual interest rate (expressed as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is compounded for
Given:
P = $100
r = 5% = 0.05
n = 12 (since the interest is compounded monthly)
t = 10
Plugging in these values in the compound interest formula, we can solve for A:
A = 100(1 + 0.05/12)^(12*10)
A ≈ 100(1.004167)^(120)
A ≈ 125.8232
Rounding this value to the nearest place value, we get $125.82.
To express $125.82 in the form of a×10^n, we need to determine the value of a and n.
$125.82 = a×10^n
To express $125.82 in scientific notation, we shift the decimal point to the left until it is between 1 and 10. In this case, we shift the decimal point 2 places to the left, giving us 1.2582.
Therefore, $125.82 can be expressed as 1.2582×10^2.
Country S has 12,345,000 residents who tested positive for COVID-19. What is the largest place value of the numeric part of this quantity?(1 point)
The largest place value of the numeric part of the quantity 12,345,000 is the "Million" place, which is represented by the digit 1 in the millions place.
To find the amount in the form of a × 10^n, we need to round the given value $15,528.23 to a single digit and then determine the corresponding power of 10.
Step 1: Round the value $15,528.23 to a single digit. Since the digit to the right of the single digit (thousands place) is less than 5, we round down to 1.
Step 2: Determine the power of 10 by counting the number of digits that need to be shifted. In this case, we need to shift 4 digits to the left to obtain the rounded value of 1.
Therefore, $15,528.23 can be expressed as 1 × 10^4.
To find the amount in the form of a×10ⁿ, we need to round $15,528.23 to the nearest place value.
$15,528.23 rounded to the nearest place value is $15,528.00. Now, we need to express this amount in the form of a×10ⁿ.
To do that, we need to determine the value of a and n.
The value of a is the first non-zero digit in the rounded amount, which is 1.
The value of n can be determined by counting the number of digits after the decimal point. In this case, there are two digits after the decimal point, so n is -2.
Therefore, the amount $15,528.23 in the form of a×10ⁿ is 1.5528 × 10⁴.