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3 years ago

What is the rational number equivalent to __ 3.24?

Mathematics

1 answer:

guajiro [1.7K]3 years ago

5 0

Answer:

$\frac{324}{100}$

Step-by-step explanation:

Think of a rational number as a fraction. The definition of a rational number is that it is the ratio of integers that, when divided, is either an integer, a decimal that terminates, or a decimal that repeats. 6/3 = 2 (6/3 is a rational number that divides to 2); 1/2 = .5 (1/2 is a rational number that divides to .5 which is a terminating decimal, meaning it ends); 1/3 = .33333333 (1/3 is a rational number that divides to .3333333 which is a repeating decimal). If we want to express 3.24 as a rational number, let's first put it into fraction form. The 4 in .24 is in the hundredths place, so as a fraction, .24 is 24/100. Check this on your calculator. Divide 24 by 100 and you get .24. So now what we have is $3\frac{24}{100}$

Now express that mixed fraction as an improper and you're done. 3 times 100 is 300; 300 + 24 = 324. Put that back over 100 and your rational number is 324/100. Check that on your calculator, as well, just to see that it's true.

You might be interested in

Use compatible numbers to estimate the quotient 2,545÷4

victus00 [196]

Answer:

600

Step-by-step explanation:

round 2,545 to 2,400 and keep 4 the same because 24 goes into 4 six times so 2400/4 equals 600

24/4 is 6 and you add the two zeros

3 0

3 years ago

a 120 degree sector of a circle has an area of 67 square centimeters. to the nearest centimeter, what is the diameter of the cir

Vitek1552 [10]

Answer:

16 cm

Step-by-step explanation:

We have to first find the radius of the circle.

The area of a sector is given as:

$A = \frac{\alpha }{360} * \pi r^2$

where α = central angle of the sector = 120°

r = radius of the circle

Therefore:

$67 = \frac{120}{360} * \pi r^2\\\\\pi r^2 = \frac{360 * 67}{120}\\ \\r^2 = \frac{360 * 67}{120 * \pi}\\\\r^2 = 63.98\\\\r = \sqrt{63.98} = 8.0 cm$

The diameter of a circle is twice its radius, therefore:

D = 2 * 8 = 16 cm

The diameter of the circle is 16 cm

8 0

3 years ago

On the 1st of January 2014 Carol invested some money in the bank account. the account pays 2.5% compound interest per year on fi

stira [4]

Answer:

The initial amount invested into the account on 1st January 2014 was £23,360

Step-by-step explanation:

In order to calculate the initial deposit in question, we will have to make use of the formula for calculating compound interest:

Fv = Pv × (1 + r)^t ------ since it was compounded annually.

Where Fv = future value

Pv = present value

r = interest rate

t = time (years)

Here, r = 2.5% or 0.025

t = 1 year

Let x represent this initial deposit. Then at the end of the year(31st Dec 2014), we will have:

Fv = x × (1 + 0.025)^1

Fv = x × (1.025)

Fv = £1.025x

Therefore, the amount that will be in the account as at 31st Dec 2014 is = £1.025x.

Now, if the owner of the account then withdraws a sum of £1,000 from the account on the 1st of Jan 2015, then the balance that will be in the account after the withdrawal will be = £1.025x - 1000. This will now be the principal or present value that will accrue interest for the year - 2015.

Again, we were told that that the future value or the balance on the 1st of Jan 2016 will be £23,517. We will then once again use the compound interest formula, making the present value (1.025x - 1000) the subject of the formula so that we can solve for x. Once "x" is determined, then we have exposed the initial deposit that was made into the account on the 1st of January 2014.

Fv = Pv × (1 + r)^t

Here,

Fv = 23,517

Pv = 1.025x - 1000

r = 0.025

t = 1

23,517 = 1.025x - 1000 × (1 + 0.025)^1

23,517 = 1.025x -1000 × (1.025)

23,517 = 1.050625x - 1025

1.050625x = 23,517 + 1025

1.050625x = 24,542

Then making "x" the subject of the formula:

x = 24,542/1.050625

x = £23,360

Therefore, the initial deposit that Carole made into the account on 1st January 2014 was £23,360

3 0

4 years ago

Can someone please help me with this

Murljashka [212]

The answer is: [C]: " 2/3, 6/9, 8/12 " .
____________________________________________

4 0

4 years ago

Read 2 more answers

What is 20% of 62.50

MAXImum [283]

It would be:

12.5

Hope this helped, If I am wrong sorry, I have not done this in a while

7 0

3 years ago