All categories

3 years ago

Why do you multiply by a power of 10 when writing a repeating decimal as a rational number

Mathematics

1 answer:

storchak [24]3 years ago

7 0

Suppose you have some repeating decimal like

x = 0.123123123...

The repeating part has a length of 3, and multiplying both sides by 10^3 = 1000 gives

1000x = 123.123123123...

The usefulness of this is that we can subtract x from this to eliminate the decimal part:

1000x - x = 123.123... - 0.123...

999x = 123

then solve for x as a fraction:

x = 123/999

and in this case the fraction reduces further to

x = 41/333

You might be interested in

What is the value of x?

Yuliya22 [10]

Answer:

Step-by-step explanation:

∠QRT and ∠SRT are supplementary angles,

therefore m∠QRT + m∠SRT = 180°.

(45x)° + m∠SRT = 180° subtract (45x)° from both sides

m∠SRT = 180° - (45x)°

We know: the sum of the measures of the angles of the triangle is equal to 180 °. Therefore we have the equation:

(180 - 45x) + (57 + x) + 25x = 180 combine like terms

(-45x + x + 25x) + (180 + 57) = 180

-19x + 237 = 180 subtract 237 from both sides

-19x = -57 divide both sides by (-19)

x = 3

4 0

3 years ago

Area of the shaded segment=

Nataly_w [17]

Answer:

Step-by-step explanation:

Because u have to multiply 6 to find the area and then u divide

5 0

3 years ago

What is 9/7 as a mixed number

Dafna11 [192]

9/7 as a mixed number is 1 2/7

3 0

3 years ago

Read 2 more answers

What is the third quartile, Q3, of the following distribution?

GREYUIT [131]

Answer:

The third quartile is:

$Q_3=29$

Step-by-step explanation:

First organize the data from lowest to highest

4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44

Notice that we have a quantity of n = 20 data

Use the following formula to calculate the third quartile $Q_3$

For a set of n data organized in the form:

$x_1, x_2, x_3, ..., x_n$

The third quartile is $Q_3$ :

$Q_3=x_{\frac{3}{4}(n+1)}$

With n=20

$Q_3=x_{\frac{3}{4}(20+1)}$

$Q_3=x_{15.75}$

The third quartile is between $x_{15}=29$ and $x_{16}=29$

Then

$Q_3 =x_{15} + 0.75*(x_{16}- x_{15})$

$Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29$

5 0

3 years ago

Read 2 more answers

What is the zero of the following function, f(x) = –(2/7) x − 10?

Stels [109]

Answer:

Step-by-step explanation:

the zeros of a function f are found by solving the equation f(x) = 0. Example 1. Find the zero of the linear function f is given by. f(x) = -2 x + 4 I hope this helps.

7 0

3 years ago

Why do you multiply by a power of 10 when writing a repeating decimal as a rational number​

Why do you multiply by a power of 10 when writing a repeating decimal as a rational number